08-ilang-propagation / 07-bond-inertia
07bond inertiaverified
Determines how the cost of a bond made by oscillator cells depends on separation and joint motion, with which factor it enters the inertia of the bound pair, and whether the pair falls like its parts.
check_bound_pair.py10 KB · raw
"""Check (ii) of 07-bond-inertia: bound level E_b(P) and its curvature from the exact
diagonalization of the effective joint contract (7.2)-(7.4) in the sector P, against
the formulas (7.10)-(7.14) of item 2.
Ring of L cells; bodies (sigma1, sigma2) = (+,+) and (+,-) with rest costs M1, M2 of their
levels, tau = 1; field c0 = tau/r, m_h = c0/ell. The members are heavy, abar*M_k > Omega_max
(square grip) and > Omega_max/2 (linear grip), Omega_max = max_q omega_q, for every r used:
no member in the branch + can decay with one or two quanta (condition (7.15), range (N_h)).
The bound levels are then not isolated (2 sum_{sigma_i=+} Mbar_i + dE > m_h): the curvature
checked is that of the formal second-order coefficients. Grips: square (4 F0 F2 = F1^2) and linear (F2 = 0).
F1 is set (proportional to c0) so that the static bond is the same for every r; two
binding strengths: a 'deep' one (a_b < ell) and a 'shallow' one (a_b > ell).
Self-energies of the single bodies are not included (they cancel in D at this order).
"""
import json
import time
from pathlib import Path
import numpy as np
from scipy.linalg import eigh
OUT = Path(__file__).parent / "output"
OUT.mkdir(exist_ok=True)
AIRY1 = 1.0187929716 # first zero of Ai'
def setup(L, ell, r, tau, M1, M2, F0, F1, F2, sg1=1, sg2=1):
c0 = tau / r; mh = c0 / ell; kap = c0**2
n = np.arange(L); qs = 2 * np.pi * n / L
om = np.sqrt(mh**2 + 4 * kap * np.sin(qs / 2)**2)
w0 = np.sum(1 / (2 * L * om)); abar = F0 + F2 * w0
Mb1, Mb2 = abar * M1, abar * M2
I1, I2 = sg1 * Mb1 / tau**2, sg2 * Mb2 / tau**2 # signed inertias (7.1)
return dict(L=L, n=n, om=om, c0=c0, mh=mh, kap=kap, tau=tau, r=r, M1=M1, M2=M2,
F0=F0, F1=F1, F2=F2, Mb1=Mb1, Mb2=Mb2, I1=I1, I2=I2, I=I1 + I2,
mred=I1 * I2 / (I1 + I2), mu12=sg1 * sg2 * M1 * M2, sg1=sg1, sg2=sg2,
rest=sg1 * Mb1 + sg2 * Mb2)
def hamiltonian(P, s, static=False):
L, n, om, tau = s["L"], s["n"], s["om"], s["tau"]
ks = 2 * np.pi * n / L
p1 = P * s["I1"] / s["I"] + ks; p2 = P * s["I2"] / s["I"] - ks
e1 = s["sg1"] * np.sqrt(s["Mb1"]**2 + tau**2 * np.sin(p1)**2)
e2 = s["sg2"] * np.sqrt(s["Mb2"]**2 + tau**2 * np.sin(p2)**2)
th1 = np.arctan2(tau * np.sin(p1), s["Mb1"]); th2 = np.arctan2(tau * np.sin(p2), s["Mb2"])
if static:
C = np.ones((L, L)); D1 = np.zeros((L, L)); D2 = np.zeros((L, L))
else:
C = np.cos((th1[:, None] + th1[None, :]) / 2) * np.cos((th2[:, None] + th2[None, :]) / 2)
D1 = e1[None, :] - e1[:, None]; D2 = e2[:, None] - e2[None, :] # rows k', cols k
m = (n[None, :] - n[:, None]) % L # q = k - k'
wq2 = om[m]**2
U = -s["mu12"] * s["F1"]**2 * C / (2 * L) * (1 / (wq2 - D1**2) + 1 / (wq2 - D2**2))
ratio = max(np.max(np.abs(D1) / np.sqrt(wq2)), np.max(np.abs(D2) / np.sqrt(wq2)))
if s["F2"] != 0:
for mi in range(L):
kp = (n - mi) % L
ob = om[(mi - n) % L]; Om = om + ob; w = Om / (om * ob)
d2 = np.concatenate([D1[kp, n], D2[kp, n]])**2
S = (1 / (Om[None, :]**2 - d2[:, None])) @ w
U[kp, n] += -s["mu12"] * s["F2"]**2 * C[kp, n] / (2 * L**2) * (S[:L] + S[L:])
ratio = max(ratio, np.sqrt(d2.max()) / Om.min())
if static:
return U, ratio # static mutual kernel only
return U + np.diag(e1 + e2), ratio
def analyse(s):
L, tau, r = s["L"], s["tau"], s["r"]
h = (0.004 if s["mred"] < 0 else 0.015) * abs(s["I"]) * tau # P <= 3h keeps the pair velocity P/I below 0.045 tau
H0, ratio = hamiltonian(0.0, s)
up = s["mred"] < 0 # bound level above the band (mixed branches)
sel = [L - 2, L - 1] if up else [0, 1]
E, V = eigh(H0, subset_by_index=sel)
if up:
E, V = E[::-1], V[:, ::-1]
E0, psi = E[0], V[:, 0]
Ps = h * np.arange(1, 4); EP = []
for P in Ps:
HP, rt = hamiltonian(P, s); ratio = max(ratio, rt)
j = L - 1 if up else 0
EP.append(eigh(HP, eigvals_only=True, subset_by_index=[j, j])[0])
EP = np.array(EP)
A = np.stack([Ps**2, Ps**4, Ps**6], axis=1)
a, b, c = np.linalg.solve(A, EP - E0)
Ipair = 1 / (2 * a)
# relative label measured from the nearest band minimum (0 or pi: the two valleys of Model D)
ks = 2 * np.pi * s["n"] / L; ks = (ks + np.pi / 2) % np.pi - np.pi / 2
T = np.sum(np.abs(psi)**2 * ks**2) / (2 * s["mred"])
w_pi = np.sum(np.abs(psi[np.abs(2 * np.pi * s["n"] / L - np.pi) < np.pi / 2])**2)
dE = E0 - s["rest"]
Ust, _ = hamiltonian(0.0, s, static=True) # static kernel U~(k-k')/L
Uexp = psi @ Ust @ psi
Uq = L * Ust[0, :] # U~(q) at q = 2 pi j / L
Ur = np.real(np.fft.ifft(Uq)) # U(r), r = 0..L-1
rr = np.where(s["n"] > L // 2, s["n"] - L, s["n"])
rUp = rr * (np.roll(Ur, -1) - np.roll(Ur, 1)) / 2
psir = np.fft.ifft(psi) * np.sqrt(L) # psi(r) = L^-1/2 sum_k psi_k e^{ikr}
rUp_exp = np.sum(np.abs(psir)**2 * rUp)
I1, I2 = s["I1"], s["I2"]
D_num = Ipair - I1 - I2
D_formula = ((2 - r**2) * dE + (1 - r**2) * T) / tau**2 + 4 * I1 * I2 * T
D_general = (3 * T + 2 * Uexp) / tau**2 - (Uexp + rUp_exp) / s["c0"]**2 + 4 * I1 * I2 * T
lam = s["mu12"] * s["F1"]**2 / (2 * s["kap"])
g = -Uq[0]
rad = np.sqrt(np.sum(np.abs(psir)**2 * rr**2))
Om_max = float(np.max(s["om"]))
thr = Om_max if s["F2"] != 0 else Om_max / 2 # no-decay threshold (7.15), heavy range
Mplus = [Mb for Mb, sg in ((s["Mb1"], s["sg1"]), (s["Mb2"], s["sg2"])) if sg > 0]
decay_margin = min(Mb - thr for Mb in Mplus) # > 0: no decay with one or two quanta
isol_lhs = 2 * sum(Mplus) + dE - s["mh"] # > 0: not isolated (necessary cond. fails)
EPf = E0 + Ps**2 / (2 * (I1 + I2 + D_formula))
return dict(r=r, F1=s["F1"], F2=s["F2"], ell=s["c0"] / s["mh"], L=L,
branches=[s["sg1"], s["sg2"]], m_red=s["mred"],
E_b0=E0, gap_to_next=abs(E[1] - E[0]), weight_pi_valley=w_pi, dE=dE, T=T,
U_exp=Uexp, virial_2T=2 * T, virial_rUp=rUp_exp, rms_size=rad,
dE_deep_asym=Ur[0] + np.sign(s["mred"]) * AIRY1
* (lam**2 / (2 * abs(s["mred"])))**(1 / 3),
dE_shallow_asym=-s["mred"] * g**2 / 2,
I1=I1, I2=I2, I_pair=Ipair, D_num=D_num, D_formula=D_formula,
D_general=D_general, D_deep_asym=(2 - r**2) * dE / tau**2,
D_shallow_asym=dE / tau**2 - 4 * I1 * I2 * dE,
rel_dev_D=abs(D_num - D_formula) / abs(D_formula),
# D at first order in dE/M: I^2 (1/I - 1/I_pair) removes the trivial D^2/I term
D_num_lin=(I1 + I2)**2 * (1 / (I1 + I2) - 1 / Ipair),
dev_over_dE=abs(D_num - D_formula) / (abs(dE) / tau**2),
dev_lin_over_dE=abs((I1 + I2)**2 * (1 / (I1 + I2) - 1 / Ipair) - D_formula)
/ (abs(dE) / tau**2),
expected_scale=abs(dE) / abs(s["rest"]) + (tau / min(s["Mb1"], s["Mb2"]) / rad)**2,
T_over_dE=T / dE,
P=list(Ps), E_b_P_num=list(EP), E_b_P_formula=list(EPf),
max_EP_dev_over_shift=float(np.max(np.abs(EP - EPf) / (EP - E0))),
quartic_coeff=b, max_transfer_over_quantum=ratio,
D_over_I=D_num / (I1 + I2), Omega_max=Om_max, decay_threshold=thr,
decay_margin=decay_margin, isolation_lhs=isol_lhs,
lattice_over_dE=4 * I1 * I2 * T / (dE / tau**2))
import sys
L = int(sys.argv[1]) if len(sys.argv) > 1 else 1024
ell = float(sys.argv[2]) if len(sys.argv) > 2 else 30.0
tau, M1, M2, F0 = 1.0, 5.0, 4.5, 1.0
results = []
t0 = time.time()
runs = [((1, 1), g) for g in ("square", "linear")] + [((1, -1), "linear")]
# (name, ell, target size a_b): deep a_b = ell/3; shallow a_b = 3 ell; very shallow a_b = 11 ell
regimes = [("deep", ell, ell / 3), ("shallow", ell, 3 * ell), ("v-shallow", 8.0, 88.0)]
for (sg1, sg2), grip in runs:
mred0 = abs((M1 * M2 / (sg1 * M1 + sg2 * M2))) / tau**2
for strength, ell_, ab in regimes:
if sg1 != sg2 and strength == "v-shallow":
continue
for r in (0.5, 1.0, 1.4):
c0 = tau / r; mh = c0 / ell_
if strength == "deep":
lam = 1 / (2 * mred0 * ab**3); F1 = c0 * np.sqrt(2 * lam / (M1 * M2))
else:
gg = 1 / (mred0 * ab); F1 = mh * np.sqrt(gg / (M1 * M2))
F2 = F1**2 / (4 * F0) if grip == "square" else 0.0
s = setup(L, ell_, r, tau, M1, M2, F0, F1, F2, sg1, sg2)
res = analyse(s); res.update(strength=strength, grip=grip)
results.append(res)
print(f"{sg1:+d}{sg2:+d} {strength:9s} {grip:6s} r={r:.2f} size={res['rms_size']:.1f} "
f"dE={res['dE']:.3e} T/dE={res['T_over_dE']:.3f} D_num={res['D_num']:.4e} "
f"D_lin={res['D_num_lin']:.4e} D_form={res['D_formula']:.4e} "
f"D_gen={res['D_general']:.4e} dev/dE={res['dev_over_dE']:.3f} "
f"devlin/dE={res['dev_lin_over_dE']:.3f} scale={res['expected_scale']:.3f} "
f"D/I={res['D_over_I']:.3f} EPdev={res['max_EP_dev_over_shift']:.3f} "
f"ratio={res['max_transfer_over_quantum']:.2f} gap={res['gap_to_next']:.2e} "
f"wpi={res['weight_pi_valley']:.2f} margin={res['decay_margin']:.3f} "
f"isol={res['isolation_lhs']:.3f} latt/dE={res['lattice_over_dE']:.3f} "
f"t={time.time() - t0:.0f}s", flush=True)
summary = {"parameters": {"L": L, "tau": tau, "M_k1": M1, "M_k2": M2, "F0": F0,
"regimes": regimes, "r": [0.5, 1.0, 1.4], "P": "h, 2h, 3h with h = 0.015 |I| tau (+,+), 0.004 |I| tau (+,-)"},
"max_dev_lin_over_dE": max(x["dev_lin_over_dE"] for x in results),
"max_dev_over_dE": max(x["dev_over_dE"] for x in results),
"min_decay_margin": min(x["decay_margin"] for x in results),
"min_isolation_lhs": min(x["isolation_lhs"] for x in results),
"results": results}
(OUT / "bound_pair_check.json").write_text(json.dumps(summary, indent=1, default=float))
print("max dev/dE:", summary["max_dev_over_dE"], " max devlin/dE:", summary["max_dev_lin_over_dE"])
check_mutual_term.py7 KB · raw
"""Check (i) of 07-bond-inertia: the mutual term (7.3)-(7.4) against second-order
perturbation theory in the total contract, restricted to at most two field quanta.
Ring of L = 16 cells, two Model D bodies (clock level fixed, so S_i -> M_i sigma_3),
grip F(q) = F0 + F1 q + F2 q^2. The unperturbed contract H0 contains the motion terms,
the first-order grip abar*M_i*sigma_3 (abar = F0 + F2 w0) and the field; the
perturbation is V = sum_i sum_x |x><x| M_i sigma_3 (dF(q_x) - F2 w0). The mutual
term is the part of the symmetric (des Cloizeaux) second-order effective contract with
one vertex on each body. Everything is built numerically in the position basis of the
bodies and the occupation basis of the field modes (<= 2 quanta).
"""
import json
from itertools import combinations_with_replacement
from pathlib import Path
import numpy as np
OUT = Path(__file__).parent / "output"
OUT.mkdir(exist_ok=True)
def fock(L):
states = [()] + [(j,) for j in range(L)] + list(combinations_with_replacement(range(L), 2))
index = {s: i for i, s in enumerate(states)}
B = np.zeros((L, len(states), len(states)))
for i, s in enumerate(states):
for j in set(s):
t = list(s); t.remove(j)
B[j, index[tuple(sorted(t))], i] = np.sqrt(s.count(j))
return states, B
def body(L, tau, Mbar):
"""Position-basis contract (index 2x+s) and its plane-wave eigenvectors."""
s1 = np.array([[0, 1], [1, 0]], complex); s3 = np.diag([1.0, -1.0]).astype(complex)
h = np.zeros((2 * L, 2 * L), complex)
for x in range(L):
y = (x + 1) % L
h[2*y:2*y+2, 2*x:2*x+2] += 0.5 * tau * (-1j * s1)
h[2*x:2*x+2, 2*y:2*y+2] += 0.5 * tau * (1j * s1)
h[2*x:2*x+2, 2*x:2*x+2] += Mbar * s3
W = np.zeros((2 * L, 2 * L), complex); e = np.zeros(2 * L); lab = []
xs = np.arange(L)
for n in range(L):
p = 2 * np.pi * n / L
pw = np.exp(1j * p * xs) / np.sqrt(L)
blk = np.array([[np.vdot(np.kron(pw, np.eye(2)[a]), h @ np.kron(pw, np.eye(2)[b]))
for b in range(2)] for a in range(2)])
ev, U = np.linalg.eigh(blk)
for col, band in ((1, +1), (0, -1)):
u = U[:, col]
ref = u[0] if band == +1 else u[1] # phase convention of Step 1
u = u * abs(ref) / ref if abs(ref) > 1e-12 else u
v = np.kron(pw, u); k = len(lab)
W[:, k] = v; e[k] = ev[col]; lab.append((n, band))
resid = np.max(np.abs(h @ W - W * e))
return W, e, lab, resid
def run(case):
L, kap, mh, tau = case["L"], case["kappa_h"], case["m_h"], case["tau"]
M1, M2, sg1, sg2 = case["M1"], case["M2"], case["sigma1"], case["sigma2"]
F0, F1, F2 = case["F0"], case["F1"], case["F2"]
qs = 2 * np.pi * np.arange(L) / L
om = np.sqrt(mh**2 + 4 * kap * np.sin(qs / 2)**2)
w0 = np.sum(1 / (2 * L * om))
abar = F0 + F2 * w0
states, B = fock(L)
EF = np.array([sum(om[j] for j in s) for s in states])
vac = np.zeros(len(states)); vac[0] = 1
X = []
for x in range(L):
qx = sum((B[j] * np.exp(1j * qs[j] * x) + B[j].T * np.exp(-1j * qs[j] * x))
/ np.sqrt(2 * L * om[j]) for j in range(L))
chi = F1 * (qx @ vac) + F2 * (qx @ (qx @ vac) - w0 * vac)
X.append(chi)
X = np.array(X) # (x, fock)
assert abs(X[:, 0]).max() < 1e-12 # no vacuum component
W1, e1, lab1, r1 = body(L, tau, abar * M1)
W2, e2, lab2, r2 = body(L, tau, abar * M2)
s3 = np.diag([1.0, -1.0])
def Y(psi1, psi2):
B1 = np.zeros((2 * L, L), complex); B2 = np.zeros((2 * L, L), complex)
for x in range(L):
B1[2*x:2*x+2, x] = M1 * s3 @ psi1[2*x:2*x+2]
B2[2*x:2*x+2, x] = M2 * s3 @ psi2[2*x:2*x+2]
V1 = np.einsum('ax,b,xc->abc', B1, psi2, X)
V2 = np.einsum('a,bx,xc->abc', psi1, B2, X)
tr = lambda T: np.einsum('ap,bq,abc->pqc', W1.conj(), W2.conj(), T)
return tr(V1), tr(V2)
En = e1[:, None, None] + e2[None, :, None] + EF[None, None, :]
idx1 = {l: i for i, l in enumerate(lab1)}; idx2 = {l: i for i, l in enumerate(lab2)}
def eps(M, sg, p):
return sg * np.sqrt((abar * M)**2 + tau**2 * np.sin(p)**2)
def th(M, p):
return np.arctan2(tau * np.sin(p), abar * M)
rows = []
for (n1, n2, m) in case["labels"]:
i1, i2 = idx1[(n1 % L, sg1)], idx2[(n2 % L, sg2)]
f1, f2 = idx1[((n1 - m) % L, sg1)], idx2[((n2 + m) % L, sg2)]
Yi = Y(W1[:, i1], W2[:, i2]); Yf = Y(W1[:, f1], W2[:, f2])
Ei, Ef = e1[i1] + e2[i2], e1[f1] + e2[f2]
cross = (Yf[0].conj() * Yi[1] + Yf[1].conj() * Yi[0])[:, :, 1:] # Q: >= 1 quantum
num = 0.5 * np.sum(cross * (1 / (Ei - En[:, :, 1:]) + 1 / (Ef - En[:, :, 1:])))
# closed form (7.3)-(7.4)
p1, p2, q = qs[n1 % L], qs[n2 % L], qs[m % L]
p1f, p2f = p1 - q, p2 + q
D1 = eps(M1, sg1, p1) - eps(M1, sg1, p1f); D2 = eps(M2, sg2, p2f) - eps(M2, sg2, p2)
c1 = np.cos((th(M1, p1) + th(M1, p1f)) / 2); c2 = np.cos((th(M2, p2) + th(M2, p2f)) / 2)
mu12 = sg1 * M1 * sg2 * M2
wq = om[m % L]
U1 = -mu12 * F1**2 * c1 * c2 / (2 * L) * (1 / (wq**2 - D1**2) + 1 / (wq**2 - D2**2))
ob = om[(m - np.arange(L)) % L]; Om = om + ob
U2 = -mu12 * F2**2 * c1 * c2 / (2 * L**2) * np.sum(Om / (om * ob) * (
1 / (Om**2 - D1**2) + 1 / (Om**2 - D2**2)))
form = U1 + U2
rows.append({"labels_n1_n2_m": [n1, n2, m], "numerical": [num.real, num.imag],
"formula": form, "rel_dev": abs(num - form) / abs(form)})
return {"case": {k: v for k, v in case.items() if k != "labels"}, "abar": abar,
"eigvec_residual": max(r1, r2), "rows": rows,
"max_rel_dev": max(r["rel_dev"] for r in rows)}
labels = [(0, 0, 1), (1, -2, 3), (3, -5, 2), (-2, 4, -1), (5, 2, 7), (2, 2, 0), (-3, 1, 0), (6, -6, 8)]
base = dict(L=16, kappa_h=1.0, m_h=0.3, tau=0.8, M1=0.7, M2=0.5, F0=1.0, F1=0.3, F2=0.2,
sigma1=1, sigma2=1, labels=labels)
cases = [base,
dict(base, F2=base["F1"]**2 / (4 * base["F0"])), # square grip
dict(base, sigma2=-1), # mixed branches
dict(base, tau=1.3)] # r > 1
res = [run(c) for c in cases]
summary = {"max_rel_dev_all": max(r["max_rel_dev"] for r in res), "cases": res}
(OUT / "mutual_term_check.json").write_text(json.dumps(summary, indent=1))
for r in res:
print(r["case"]["tau"], r["case"]["F2"], r["case"]["sigma2"], "max rel dev", r["max_rel_dev"],
"resid", r["eigvec_residual"])
print("overall", summary["max_rel_dev_all"])
output/bound_pair_check.json44 KB · raw
{
"parameters": {
"L": 1024,
"tau": 1.0,
"M_k1": 5.0,
"M_k2": 4.5,
"F0": 1.0,
"regimes": [
[
"deep",
30.0,
10.0
],
[
"shallow",
30.0,
90.0
],
[
"v-shallow",
8.0,
88.0
]
],
"r": [
0.5,
1.0,
1.4
],
"P": "h, 2h, 3h with h = 0.015 |I| tau (+,+), 0.004 |I| tau (+,-)"
},
"max_dev_lin_over_dE": 0.06679796736019555,
"max_dev_over_dE": 0.05078432660915525,
"min_decay_margin": 0.49220007306822744,
"min_isolation_lhs": 9.93333408345031,
"results": [
{
"r": 0.5,
"F1": 0.008663817195385747,
"F2": 1.8765432098765437e-05,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684404353262782,
"E_b0": 9.495632602875338,
"gap_to_next": 9.344415126122385e-06,
"weight_pi_valley": 0.49999999966668845,
"dE": -0.004445143266734064,
"T": 0.0005541382419848246,
"U_exp": -0.00499787334759333,
"virial_2T": 0.0011082764839696491,
"virial_rUp": 0.0010893011623473825,
"rms_size": 9.98006716832386,
"dE_deep_asym": -0.004181681896021511,
"dE_shallow_asym": -0.17100152717982506,
"I1": 5.000040919022143,
"I2": 4.500036827119929,
"I_pair": 9.542634011994519,
"D_num": 0.042556265852446984,
"D_formula": 0.04250986103929819,
"D_general": 0.04251706915167349,
"D_deep_asym": -0.007779000716784612,
"D_shallow_asym": 0.39562429883909317,
"rel_dev_D": 0.0010916246728233801,
"D_num_lin": 0.042366482218176564,
"dev_over_dE": 0.010439441512733467,
"dev_lin_over_dE": 0.032255163111305496,
"expected_scale": 0.0009636996104100159,
"T_over_dE": -0.1246615032932248,
"P": [
0.14250116619213107,
0.28500233238426215,
0.42750349857639325
],
"E_b_P_num": [
9.496694700412077,
9.499858313070535,
9.505055849597985
],
"E_b_P_formula": [
9.496696600566636,
9.499888593640533,
9.505208582097028
],
"max_EP_dev_over_shift": 0.016208054775389804,
"quartic_coeff": -0.004598503843155842,
"max_transfer_over_quantum": 0.053978503594318474,
"D_over_I": 0.004479570271909495,
"Omega_max": 4.000555516980667,
"decay_threshold": 4.000555516980667,
"decay_margin": 0.4994813101392621,
"isolation_lhs": 18.92904368235074,
"lattice_over_dE": -11.219718934106949,
"strength": "deep",
"grip": "square"
},
{
"r": 1.0,
"F1": 0.004331908597692873,
"F2": 4.691358024691359e-06,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684307439789287,
"E_b0": 9.495593540353218,
"gap_to_next": 9.34640275929155e-06,
"weight_pi_valley": 0.4999999996708749,
"dE": -0.004445332717819994,
"T": 0.00055430834976424,
"U_exp": -0.004998037762256389,
"virial_2T": 0.00110861669952848,
"virial_rUp": 0.001089188598691539,
"rms_size": 9.978812715136398,
"dE_deep_asym": -0.004181675310344159,
"dE_shallow_asym": -0.17100076358964525,
"I1": 5.000020459511072,
"I2": 4.500018413559965,
"I_pair": 9.545485742995986,
"D_num": 0.04544686992494906,
"D_formula": 0.04544282703339841,
"D_general": 0.045463858439563194,
"D_deep_asym": -0.004445332717819994,
"D_shallow_asym": 0.3956378860687008,
"rel_dev_D": 8.8966550159481e-05,
"D_num_lin": 0.04523049350979431,
"dev_over_dE": 0.0009094688310840557,
"dev_lin_over_dE": 0.0477654963267246,
"expected_scale": 0.0009638501875769622,
"T_over_dE": -0.12469445707453697,
"P": [
0.14250058309606556,
0.2850011661921311,
0.4275017492881967
],
"E_b_P_num": [
9.496655313074937,
9.499817972236158,
9.505013988183846
],
"E_b_P_formula": [
9.496657206746423,
9.499848205926039,
9.505166537892068
],
"max_EP_dev_over_shift": 0.01619346669762423,
"quartic_coeff": -0.004594303799778412,
"max_transfer_over_quantum": 0.10795743831781858,
"D_over_I": 0.004783861469638139,
"Omega_max": 2.0002777584903333,
"decay_threshold": 2.0002777584903333,
"decay_margin": 2.4997406550696315,
"isolation_lhs": 18.96229908009092,
"lattice_over_dE": -11.222592979650738,
"strength": "deep",
"grip": "square"
},
{
"r": 1.4,
"F1": 0.003094220426923481,
"F2": 2.393550012597632e-06,
"ell": 29.999999999999996,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.368427975022543,
"E_b0": 9.495582186931008,
"gap_to_next": 9.349002265679474e-06,
"weight_pi_valley": 0.49999999979671716,
"dE": -0.004445579548303158,
"T": 0.0005545263638128549,
"U_exp": -0.004998252400528394,
"virial_2T": 0.0011090527276257098,
"virial_rUp": 0.0010890438360171362,
"rms_size": 9.977186399081914,
"dE_deep_asym": -0.004181673428719119,
"dE_shallow_asym": -0.17100054542112053,
"I1": 5.00001461393648,
"I2": 4.500013152542832,
"I_pair": 9.549181320298219,
"D_num": 0.049153553818907625,
"D_formula": 0.049197495989660875,
"D_general": 0.049236787557677186,
"D_deep_asym": -0.00017782318193212745,
"D_shallow_asym": 0.3956589186294158,
"rel_dev_D": 0.0008931790098114894,
"D_num_lin": 0.04890054031209617,
"dev_over_dE": 0.009884463943519444,
"dev_lin_over_dE": 0.06679796736019555,
"expected_scale": 0.0009640395639798536,
"T_over_dE": -0.12473657434034965,
"P": [
0.14250041649718967,
0.28500083299437934,
0.427501249491569
],
"E_b_P_num": [
9.49664354765134,
9.499804996194582,
9.504999077909405
],
"E_b_P_formula": [
9.496645433851242,
9.499835174611942,
9.50515140921311
],
"max_EP_dev_over_shift": 0.01617639028144892,
"quartic_coeff": -0.004589155914633905,
"max_transfer_over_quantum": 0.15114058609743092,
"D_over_I": 0.00517404317409946,
"Omega_max": 1.428769827493095,
"decay_threshold": 1.428769827493095,
"decay_margin": 3.071243325049737,
"isolation_lhs": 18.971800429600794,
"lattice_over_dE": -11.226357314852839,
"strength": "deep",
"grip": "square"
},
{
"r": 0.5,
"F1": 0.0009626463550428607,
"F2": 2.3167200121932636e-07,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684212919241063,
"E_b0": 9.499986707664469,
"gap_to_next": 1.5392560115401466e-08,
"weight_pi_valley": 0.49999979648056453,
"dE": -1.4252164445949234e-05,
"T": 8.427985646079244e-06,
"U_exp": -2.267930869352967e-05,
"virial_2T": 1.685597129215849e-05,
"virial_rUp": 1.6957269900149444e-05,
"rms_size": 93.354107085166,
"dE_deep_asym": 3.670929182480144e-05,
"dE_shallow_asym": -2.6063103010830508e-05,
"I1": 5.000000505173113,
"I2": 4.500000454655802,
"I_pair": 9.50074144648759,
"D_num": 0.000740486658674655,
"D_formula": 0.0007398985628745909,
"D_general": 0.0007398747106699661,
"D_deep_asym": -2.494128778041116e-05,
"D_shallow_asym": 0.001268442894882665,
"rel_dev_D": 0.0007948330076210514,
"D_num_lin": 0.0007404289452324397,
"dev_over_dE": 0.041263613137108725,
"dev_lin_over_dE": 0.03721416209167974,
"expected_scale": 7.166638086041099e-06,
"T_over_dE": -0.5913477688278187,
"P": [
0.14250001439743373,
0.28500002879486747,
0.42750004319230117
],
"E_b_P_num": [
9.501053491768287,
9.504231314511776,
9.50945305896286
],
"E_b_P_formula": [
9.501055374540345,
9.50426137516797,
9.509604709547343
],
"max_EP_dev_over_shift": 0.016019961620137742,
"quartic_coeff": -0.004569040863871245,
"max_transfer_over_quantum": 0.05397892940243092,
"D_over_I": 7.794595619577604e-05,
"Omega_max": 4.000555516980667,
"decay_threshold": 4.000555516980667,
"decay_margin": 0.4994449376751353,
"isolation_lhs": 18.93332100082672,
"lattice_over_dE": -53.221309948891985,
"strength": "shallow",
"grip": "square"
},
{
"r": 1.0,
"F1": 0.00048132317752143036,
"F2": 5.791800030483159e-08,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684211722778423,
"E_b0": 9.499986227732892,
"gap_to_next": 1.5392611629749808e-08,
"weight_pi_valley": 0.49999989555524194,
"dE": -1.4252181564700095e-05,
"T": 8.428011733867782e-06,
"U_exp": -2.2679334266465274e-05,
"virial_2T": 1.6856023467735563e-05,
"virial_rUp": 1.6957271315112325e-05,
"rms_size": 93.35404416640613,
"dE_deep_asym": 3.670929431604563e-05,
"dE_shallow_asym": -2.606310157400235e-05,
"I1": 5.000000252586556,
"I2": 4.5000002273279005,
"I_pair": 9.500745241077524,
"D_num": 0.0007447611630677642,
"D_formula": 0.0007442689511202907,
"D_general": 0.0007441685623050165,
"D_deep_asym": -1.4252181564700095e-05,
"D_shallow_asym": 0.0012684442888550522,
"rel_dev_D": 0.0006613361295437904,
"D_num_lin": 0.0007447027814172299,
"dev_over_dE": 0.03453590211709228,
"dev_lin_over_dE": 0.030439571301405302,
"expected_scale": 7.166648174403929e-06,
"T_over_dE": -0.5913488889828867,
"P": [
0.14250000719871683,
0.28500001439743367,
0.4275000215961505
],
"E_b_P_num": [
9.501053011300426,
9.504230832416601,
9.509452574089321
],
"E_b_P_formula": [
9.501054894063184,
9.504260893054063,
9.509604224705525
],
"max_EP_dev_over_shift": 0.016019973334312734,
"quartic_coeff": -0.004569045362014492,
"max_transfer_over_quantum": 0.10795786412750073,
"D_over_I": 7.839590794151944e-05,
"Omega_max": 2.0002777584903333,
"decay_threshold": 2.0002777584903333,
"decay_margin": 2.499722468837567,
"isolation_lhs": 18.966653374314014,
"lattice_over_dE": -53.221405385664,
"strength": "shallow",
"grip": "square"
},
{
"r": 1.4,
"F1": 0.0003438022696581646,
"F2": 2.955000015552633e-08,
"ell": 29.999999999999996,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684211380931957,
"E_b0": 9.499986090592074,
"gap_to_next": 1.5392684460380224e-08,
"weight_pi_valley": 0.5000000802121399,
"dE": -1.4252203966336197e-05,
"T": 8.428045319481542e-06,
"U_exp": -2.2679367675883477e-05,
"virial_2T": 1.6856090638963084e-05,
"virial_rUp": 1.6957273468031274e-05,
"rms_size": 93.3539596747836,
"dE_deep_asym": 3.6709295027829726e-05,
"dE_shallow_asym": -2.6063101163480033e-05,
"I1": 5.000000180418969,
"I2": 4.500000162377072,
"I_pair": 9.500750575673276,
"D_num": 0.0007502328772357458,
"D_formula": 0.0007498631218288368,
"D_general": 0.0007496648387482604,
"D_deep_asym": -5.700881586534515e-07,
"D_shallow_asym": 0.001268446245573169,
"rel_dev_D": 0.0004930972015362995,
"D_num_lin": 0.0007501736346147948,
"dev_over_dE": 0.025943735283499834,
"dev_lin_over_dE": 0.021787001273027337,
"expected_scale": 7.166660974683179e-06,
"T_over_dE": -0.5913503160205006,
"P": [
0.1425000051419406,
0.2850000102838812,
0.42750001542582183
],
"E_b_P_num": [
9.501052873526413,
9.504230692714662,
9.509452431073958
],
"E_b_P_formula": [
9.501054756277696,
9.50426075333456,
9.509604081762669
],
"max_EP_dev_over_shift": 0.016019990935347977,
"quartic_coeff": -0.004569051160203959,
"max_transfer_over_quantum": 0.15114101190756066,
"D_over_I": 7.897187896468405e-05,
"Omega_max": 1.428769827493095,
"decay_threshold": 1.428769827493095,
"decay_margin": 3.071230334883977,
"isolation_lhs": 18.97617690957859,
"lattice_over_dE": -53.22153228271443,
"strength": "shallow",
"grip": "square"
},
{
"r": 0.5,
"F1": 0.0036507152259598386,
"F2": 3.331930415263749e-06,
"ell": 8.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684236623887247,
"E_b0": 9.499988549014567,
"gap_to_next": 3.3049329850598497e-07,
"weight_pi_valley": 0.5000000081271513,
"dE": -2.1919011317095283e-05,
"T": 1.773205857882984e-05,
"U_exp": -3.964324404608369e-05,
"virial_2T": 3.546411715765968e-05,
"virial_rUp": 3.5108410116901245e-05,
"rms_size": 70.47153414925877,
"dE_deep_asym": 0.0003801564379199276,
"dE_shallow_asym": -2.7261282524060525e-05,
"I1": 5.000005509487307,
"I2": 4.500004958538577,
"I_pair": 9.501581709536886,
"D_num": 0.001571241511001631,
"D_formula": 0.0015708295632296892,
"D_general": 0.0015709321852271012,
"D_deep_asym": -3.8358269804916745e-05,
"D_shallow_asym": 0.0019507963546744026,
"rel_dev_D": 0.0002622485478913134,
"D_num_lin": 0.0015709816805899478,
"dev_over_dE": 0.018794085462259965,
"dev_lin_over_dE": 0.006939973617333336,
"expected_scale": 1.2250928605978836e-05,
"T_over_dE": -0.8089807666187975,
"P": [
0.14250015702038826,
0.2850003140407765,
0.4275004710611648
],
"E_b_P_num": [
9.501055239975566,
9.504232773600457,
9.509454000988532
],
"E_b_P_formula": [
9.50105712350311,
9.504262846968738,
9.509605719411452
],
"max_EP_dev_over_shift": 0.01602865064841791,
"quartic_coeff": -0.004570883289043562,
"max_transfer_over_quantum": 0.05156265580506626,
"D_over_I": 0.00016539366101647434,
"Omega_max": 4.00780488547035,
"decay_threshold": 4.00780488547035,
"decay_margin": 0.49220007306822744,
"isolation_lhs": 18.74999901704045,
"lattice_over_dE": -72.80842945027374,
"strength": "v-shallow",
"grip": "square"
},
{
"r": 1.0,
"F1": 0.0018253576129799193,
"F2": 8.329826038159372e-07,
"ell": 8.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684223575101524,
"E_b0": 9.499983314893745,
"gap_to_next": 3.30497645251171e-07,
"weight_pi_valley": 0.5000000036967603,
"dE": -2.1919119197022496e-05,
"T": 1.7732260635631566e-05,
"U_exp": -3.9643432657423736e-05,
"virial_2T": 3.546452127126313e-05,
"virial_rUp": 3.5108455908251645e-05,
"rms_size": 70.47137499477384,
"dE_deep_asym": 0.0003801565919758727,
"dE_shallow_asym": -2.7261265688108215e-05,
"I1": 5.0000027547436545,
"I2": 4.5000024792692885,
"I_pair": 9.501579583453951,
"D_num": 0.0015743494410083159,
"D_formula": 0.0015739860965322714,
"D_general": 0.0015743501090705132,
"D_deep_asym": -2.1919119197022496e-05,
"D_shallow_asym": 0.0019508037822715636,
"rel_dev_D": 0.00023084351052715739,
"D_num_lin": 0.0015740885816281941,
"dev_over_dE": 0.016576600217302694,
"dev_lin_over_dE": 0.004675602837938952,
"expected_scale": 1.2250997104034367e-05,
"T_over_dE": -0.8089860033262798,
"P": [
0.14250007851019414,
0.2850001570203883,
0.4275002355305824
],
"E_b_P_num": [
9.501050004916488,
9.504227535726374,
9.509448758411454
],
"E_b_P_formula": [
9.501051888438468,
9.50425760907264,
9.509600476796258
],
"max_EP_dev_over_shift": 0.016028660941341488,
"quartic_coeff": -0.004570893055873586,
"max_transfer_over_quantum": 0.10312536703862278,
"D_over_I": 0.00016572090248662816,
"Omega_max": 2.003902442735175,
"decay_threshold": 2.003902442735175,
"decay_margin": 2.4961000365341137,
"isolation_lhs": 18.874988548906686,
"lattice_over_dE": -72.80882052715342,
"strength": "v-shallow",
"grip": "square"
},
{
"r": 1.4,
"F1": 0.001303826866414228,
"F2": 4.249911243958863e-07,
"ell": 8.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.368421984687702,
"E_b0": 9.499981819312081,
"gap_to_next": 3.3050351788688204e-07,
"weight_pi_valley": 0.4999999879996247,
"dE": -2.1919268592185404e-05,
"T": 1.7732527049850634e-05,
"U_exp": -3.9643692948005054e-05,
"virial_2T": 3.546505409970127e-05,
"virial_rUp": 3.510852908087305e-05,
"rms_size": 70.47113315473024,
"dE_deep_asym": 0.00038015663599187406,
"dE_shallow_asym": -2.7261260877836486e-05,
"I1": 5.000001967674038,
"I2": 4.500001770906635,
"I_pair": 9.501582070045483,
"D_num": 0.0015783314648105673,
"D_formula": 0.0015780286938812521,
"D_general": 0.0015787278070259168,
"D_deep_asym": -8.767707436874217e-07,
"D_shallow_asym": 0.0019508164573839334,
"rel_dev_D": 0.00019186655508175813,
"D_num_lin": 0.0015780692842389994,
"dev_over_dE": 0.013813003296246169,
"dev_lin_over_dE": 0.0018518116868977157,
"expected_scale": 1.2251084572677414e-05,
"T_over_dE": -0.8089926438591379,
"P": [
0.1425000560787101,
0.2850001121574202,
0.42750016823613035
],
"E_b_P_num": [
9.501048508715783,
9.504226037631227,
9.509447257022417
],
"E_b_P_formula": [
9.501050392233928,
9.504256110999467,
9.509598975608698
],
"max_EP_dev_over_shift": 0.01602869206093475,
"quartic_coeff": -0.004570903068934632,
"max_transfer_over_quantum": 0.1443755360254829,
"D_over_I": 0.00016614008880867814,
"Omega_max": 1.431358887667982,
"decay_threshold": 1.431358887667982,
"decay_margin": 3.0686428832386525,
"isolation_lhs": 18.91069984360704,
"lattice_over_dE": -72.8093952533513,
"strength": "v-shallow",
"grip": "square"
},
{
"r": 0.5,
"F1": 0.008663817195385747,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.495554864885632,
"gap_to_next": 9.344320492488123e-06,
"weight_pi_valley": 0.4999999997058396,
"dE": -0.0044451351143681705,
"T": 0.0005541385976927028,
"U_exp": -0.004997865567894982,
"virial_2T": 0.0011082771953854055,
"virial_rUp": 0.00108930204900347,
"rms_size": 9.980104846630304,
"dE_deep_asym": -0.004181668724650804,
"dE_shallow_asym": -0.1710000000000001,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.542555494530268,
"D_num": 0.042555494530267524,
"D_formula": 0.042509091290468475,
"D_general": 0.042516299329354273,
"D_deep_asym": -0.0077789864501442985,
"D_shallow_asym": 0.3956170251787672,
"rel_dev_D": 0.0010916074277375525,
"D_num_lin": 0.04236571621399182,
"dev_over_dE": 0.01043910670995314,
"dev_lin_over_dE": 0.03225437985298042,
"expected_scale": 0.0009637069528716993,
"T_over_dE": -0.12466181194392507,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.496616953807711,
9.499780541167235,
9.504978037329861
],
"E_b_P_formula": [
9.496618853916491,
9.499810821009065,
9.505130766163358
],
"max_EP_dev_over_shift": 0.016207793543046394,
"quartic_coeff": -0.004598543662610558,
"max_transfer_over_quantum": 0.05397893472507324,
"D_over_I": 0.00447952574002816,
"Omega_max": 4.000555516980667,
"decay_threshold": 2.0002777584903333,
"decay_margin": 2.4997222415096667,
"isolation_lhs": 18.928888198218967,
"lattice_over_dE": -11.219563074953257,
"strength": "deep",
"grip": "linear"
},
{
"r": 1.0,
"F1": 0.004331908597692873,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.495554671357684,
"gap_to_next": 9.346355435368991e-06,
"weight_pi_valley": 0.5000000001133057,
"dE": -0.004445328642315616,
"T": 0.0005543085282499393,
"U_exp": -0.004998033873035255,
"virial_2T": 0.0011086170564998787,
"virial_rUp": 0.0010891890416032898,
"rms_size": 9.978831547908575,
"dE_deep_asym": -0.004181668724650804,
"dE_shallow_asym": -0.1710000000000001,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.545446481217843,
"D_num": 0.04544648121784256,
"D_formula": 0.045442438900178926,
"D_general": 0.045463470212605814,
"D_deep_asym": -0.004445328642315616,
"D_shallow_asym": 0.3956342491660898,
"rel_dev_D": 8.895468116299331e-05,
"D_num_lin": 0.04523010761403559,
"dev_over_dE": 0.0009093405659943597,
"dev_lin_over_dE": 0.04776503678988487,
"expected_scale": 0.0009638538599367195,
"T_over_dE": -0.12469461154646927,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.496616439772385,
9.499779086284892,
9.5049750820508
],
"E_b_P_formula": [
9.496618333421019,
9.499809319611021,
9.505127629927694
],
"max_EP_dev_over_shift": 0.016193336136129156,
"quartic_coeff": -0.004594323675719618,
"max_transfer_over_quantum": 0.10795786945014647,
"D_over_I": 0.004783840128193954,
"Omega_max": 2.0002777584903333,
"decay_threshold": 1.0001388792451666,
"decay_margin": 3.4998611207548334,
"isolation_lhs": 18.96222133802435,
"lattice_over_dE": -11.222515039182234,
"strength": "deep",
"grip": "linear"
},
{
"r": 1.4,
"F1": 0.003094220426923481,
"F2": 0.0,
"ell": 29.999999999999996,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.495554423362142,
"gap_to_next": 9.34896846160882e-06,
"weight_pi_valley": 0.5000000002315309,
"dE": -0.00444557663785794,
"T": 0.0005545264918835648,
"U_exp": -0.004998249623093053,
"virial_2T": 0.0011090529837671295,
"virial_rUp": 0.0010890441519983032,
"rms_size": 9.97719984515801,
"dE_deep_asym": -0.004181668724650802,
"dE_shallow_asym": -0.17099999999999996,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.549153273320618,
"D_num": 0.04915327332061814,
"D_formula": 0.04919721577179829,
"D_general": 0.049236507222331125,
"D_deep_asym": -0.00017782306551431874,
"D_shallow_asym": 0.39565632076935664,
"rel_dev_D": 0.0008931897972432921,
"D_num_lin": 0.04890026195835614,
"dev_over_dE": 0.009884533494696488,
"dev_lin_over_dE": 0.06679759177095955,
"expected_scale": 0.0009640421881200863,
"T_over_dE": -0.1247366848118849,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.496615781006321,
9.49977722051545,
9.504971287815279
],
"E_b_P_formula": [
9.49661766718993,
9.499807398673294,
9.505123617812234
],
"max_EP_dev_over_shift": 0.016176297079987852,
"quartic_coeff": -0.004589170090628808,
"max_transfer_over_quantum": 0.15114101723020504,
"D_over_I": 0.005174028770591383,
"Omega_max": 1.428769827493095,
"decay_threshold": 0.7143849137465474,
"decay_margin": 3.7856150862534523,
"isolation_lhs": 18.97174489955262,
"lattice_over_dE": -11.22630163306964,
"strength": "deep",
"grip": "linear"
},
{
"r": 0.5,
"F1": 0.0009626463550428607,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.499985747836524,
"gap_to_next": 1.5392558339044626e-08,
"weight_pi_valley": 0.4999999282598162,
"dE": -1.42521634760584e-05,
"T": 8.427985268022157e-06,
"U_exp": -2.267930734252295e-05,
"virial_2T": 1.6855970536044313e-05,
"virial_rUp": 1.695726921299205e-05,
"rms_size": 93.35411498148571,
"dE_deep_asym": 3.670929680728992e-05,
"dE_shallow_asym": -2.606310013717422e-05,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.500740486486212,
"D_num": 0.0007404864862117222,
"D_formula": 0.0007398983769899086,
"D_general": 0.0007398745247733974,
"D_deep_asym": -2.49412860831022e-05,
"D_shallow_asym": 0.0012684425493691975,
"rel_dev_D": 0.0007948513472974184,
"D_num_lin": 0.0007404287727895247,
"dev_over_dE": 0.04126455767936858,
"dev_lin_over_dE": 0.03721510776290558,
"expected_scale": 7.166638321947422e-06,
"T_over_dE": -0.5913477825440305,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.50105253183294,
9.5042303542609,
9.509452098208106
],
"E_b_P_formula": [
9.50105441460444,
9.504260414908185,
9.50960374874776
],
"max_EP_dev_over_shift": 0.016019958452869035,
"quartic_coeff": -0.0045690413523750036,
"max_transfer_over_quantum": 0.05397893472507324,
"D_over_I": 7.794594591702339e-05,
"Omega_max": 4.000555516980667,
"decay_threshold": 2.0002777584903333,
"decay_margin": 2.4997222415096667,
"isolation_lhs": 18.93331908116986,
"lattice_over_dE": -53.22130042896275,
"strength": "shallow",
"grip": "linear"
},
{
"r": 1.0,
"F1": 0.00048132317752143036,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.49998574781892,
"gap_to_next": 1.5392611629749808e-08,
"weight_pi_valley": 0.5000001325527001,
"dE": -1.4252181079754678e-05,
"T": 8.428011544080795e-06,
"U_exp": -2.2679333590203608e-05,
"virial_2T": 1.685602308816159e-05,
"virial_rUp": 1.6957270971204724e-05,
"rms_size": 93.35404811904266,
"dE_deep_asym": 3.670929680728992e-05,
"dE_shallow_asym": -2.606310013717422e-05,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.500744761030381,
"D_num": 0.0007447610303810137,
"D_formula": 0.0007442688578875169,
"D_general": 0.0007441684690381056,
"D_deep_asym": -1.4252181079754678e-05,
"D_shallow_asym": 0.0012684441160981663,
"rel_dev_D": 0.0006612832020055315,
"D_num_lin": 0.0007447026487482009,
"dev_over_dE": 0.03453313501580411,
"dev_lin_over_dE": 0.03043680530415138,
"expected_scale": 7.166648291813545e-06,
"T_over_dE": -0.5913488957878064,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.501052531332757,
9.504230352291165,
9.509452093711948
],
"E_b_P_formula": [
9.501054414095233,
9.504260412924172,
9.509603744305736
],
"max_EP_dev_over_shift": 0.01601997175057987,
"quartic_coeff": -0.004569045610664911,
"max_transfer_over_quantum": 0.10795786945014647,
"D_over_I": 7.839589793484354e-05,
"Omega_max": 2.0002777584903333,
"decay_threshold": 1.0001388792451666,
"decay_margin": 3.4998611207548334,
"isolation_lhs": 18.966652414485583,
"lattice_over_dE": -53.22140062090257,
"strength": "shallow",
"grip": "linear"
},
{
"r": 1.4,
"F1": 0.0003438022696581646,
"F2": 0.0,
"ell": 29.999999999999996,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.499985747796382,
"gap_to_next": 1.5392682684023384e-08,
"weight_pi_valley": 0.5000000620166365,
"dE": -1.4252203618170256e-05,
"T": 8.428045183957283e-06,
"U_exp": -2.267936719287719e-05,
"virial_2T": 1.6856090367914567e-05,
"virial_rUp": 1.6957273222298614e-05,
"rms_size": 93.35396250348191,
"dE_deep_asym": 3.670929680728993e-05,
"dE_shallow_asym": -2.606310013717422e-05,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.500750232846745,
"D_num": 0.0007502328467445807,
"D_formula": 0.0007498630550348297,
"D_general": 0.0007496647719046069,
"D_deep_asym": -5.700881447268139e-07,
"D_shallow_asym": 0.0012684461220171528,
"rel_dev_D": 0.0004931456580879478,
"D_num_lin": 0.0007501736041257215,
"dev_over_dE": 0.02594628309123647,
"dev_lin_over_dE": 0.021789549125993922,
"expected_scale": 7.166661057706199e-06,
"T_over_dE": -0.5913503209575462,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.50105253069236,
9.504230349767921,
9.509452087947261
],
"E_b_P_formula": [
9.501054413443446,
9.50426041038464,
9.509603738619962
],
"max_EP_dev_over_shift": 0.016019989804222957,
"quartic_coeff": -0.004569051332162315,
"max_transfer_over_quantum": 0.15114101723020504,
"D_over_I": 7.89718786046927e-05,
"Omega_max": 1.428769827493095,
"decay_threshold": 0.7143849137465474,
"decay_margin": 3.7856150862534523,
"isolation_lhs": 18.976176223986855,
"lattice_over_dE": -53.221528886179165,
"strength": "shallow",
"grip": "linear"
},
{
"r": 0.5,
"F1": 0.0036507152259598386,
"F2": 0.0,
"ell": 8.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.499978081011127,
"gap_to_next": 3.3049273007179636e-07,
"weight_pi_valley": 0.5000000065486869,
"dE": -2.1918988872826617e-05,
"T": 1.7732043496556667e-05,
"U_exp": -3.964320653623254e-05,
"virial_2T": 3.5464086993113333e-05,
"virial_rUp": 3.5108380873713736e-05,
"rms_size": 70.47161033680031,
"dE_deep_asym": 0.00038015674603190973,
"dE_shallow_asym": -2.7261248852157948e-05,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.501571236713591,
"D_num": 0.001571236713591162,
"D_formula": 0.0015708247167850707,
"D_general": 0.0015709273385229345,
"D_deep_asym": -3.835823052744658e-05,
"D_shallow_asym": 0.001950790009681569,
"rel_dev_D": 0.00026228057254823196,
"D_num_lin": 0.0015709768844793214,
"dev_over_dE": 0.018796341769307744,
"dev_lin_over_dE": 0.006942277088305061,
"expected_scale": 1.2250929199179619e-05,
"T_over_dE": -0.8089809068948164,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.501044770801107,
9.504222300985752,
9.509443522880366
],
"E_b_P_formula": [
9.501046654322561,
9.504252374256867,
9.50959524081404
],
"max_EP_dev_over_shift": 0.016028616072023116,
"quartic_coeff": -0.004570888639160199,
"max_transfer_over_quantum": 0.05156271123358484,
"D_over_I": 0.0001653933382727539,
"Omega_max": 4.00780488547035,
"decay_threshold": 2.003902442735175,
"decay_margin": 2.496097557264825,
"isolation_lhs": 18.74997808101113,
"lattice_over_dE": -72.80828162053348,
"strength": "v-shallow",
"grip": "linear"
},
{
"r": 1.0,
"F1": 0.0018253576129799193,
"F2": 0.0,
"ell": 8.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.499978080892026,
"gap_to_next": 3.304973610340767e-07,
"weight_pi_valley": 0.5000000046718449,
"dE": -2.1919107973999985e-05,
"T": 1.7732253092744014e-05,
"U_exp": -3.964341390074759e-05,
"virial_2T": 3.546450618548803e-05,
"virial_rUp": 3.510844128513223e-05,
"rms_size": 70.47141309754875,
"dE_deep_asym": 0.00038015674603190973,
"dE_shallow_asym": -2.7261248852157948e-05,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.50157434698127,
"D_num": 0.001574346981270125,
"D_formula": 0.0015739836703729613,
"D_general": 0.0015743476824393134,
"D_deep_asym": -2.1919107973999985e-05,
"D_shallow_asym": 0.0019508006096859987,
"rel_dev_D": 0.00023082253266171467,
"D_num_lin": 0.0015740861225600061,
"dev_over_dE": 0.01657507675926505,
"dev_lin_over_dE": 0.004674103853421754,
"expected_scale": 1.2250997397984197e-05,
"T_over_dE": -0.8089860734194869,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.501044770329264,
9.504222299419022,
9.509443519357378
],
"E_b_P_formula": [
9.501046653848196,
9.504252372716707,
9.509595237497557
],
"max_EP_dev_over_shift": 0.016028643652851338,
"quartic_coeff": -0.004570895737347148,
"max_transfer_over_quantum": 0.10312542246716969,
"D_over_I": 0.00016572073487053948,
"Omega_max": 2.003902442735175,
"decay_threshold": 1.0019512213675874,
"decay_margin": 3.4980487786324126,
"isolation_lhs": 18.874978080892028,
"lattice_over_dE": -72.80874660775383,
"strength": "v-shallow",
"grip": "linear"
},
{
"r": 1.4,
"F1": 0.001303826866414228,
"F2": 0.0,
"ell": 8.0,
"L": 1024,
"branches": [
1,
1
],
"m_red": 2.3684210526315788,
"E_b0": 9.49997808073943,
"gap_to_next": 3.3050331182948867e-07,
"weight_pi_valley": 0.5000000052203085,
"dE": -2.1919260570157917e-05,
"T": 1.7732521660336475e-05,
"U_exp": -3.964367954864392e-05,
"virial_2T": 3.546504332067295e-05,
"virial_rUp": 3.5108518634504636e-05,
"rms_size": 70.47116038056568,
"dE_deep_asym": 0.00038015674603190973,
"dE_shallow_asym": -2.7261248852157948e-05,
"I1": 5.0,
"I2": 4.5,
"I_pair": 9.501578329836722,
"D_num": 0.0015783298367217924,
"D_formula": 0.0015780269582135534,
"D_general": 0.0015787260707057175,
"D_deep_asym": -8.767704228063223e-07,
"D_shallow_asym": 0.0019508141907440546,
"rel_dev_D": 0.00019193493917359585,
"D_num_lin": 0.0015780676565875437,
"dev_over_dE": 0.013817916314721321,
"dev_lin_over_dE": 0.0018567402791749906,
"expected_scale": 1.2251084779334877e-05,
"T_over_dE": -0.8089926940545842,
"P": [
0.1425,
0.285,
0.4275
],
"E_b_P_num": [
9.501044769724905,
9.504222297411697,
9.509443514840937
],
"E_b_P_formula": [
9.50104665324088,
9.504252370745235,
9.50959523325249
],
"max_EP_dev_over_shift": 0.016028679712533068,
"quartic_coeff": -0.004570904970841788,
"max_transfer_over_quantum": 0.14437559145403758,
"D_over_I": 0.00016613998281282024,
"Omega_max": 1.431358887667982,
"decay_threshold": 0.715679443833991,
"decay_margin": 3.784320556166009,
"isolation_lhs": 18.910692366453716,
"lattice_over_dE": -72.80934246491258,
"strength": "v-shallow",
"grip": "linear"
},
{
"r": 0.5,
"F1": 0.001987615979999813,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
-1
],
"m_red": -45.0,
"E_b0": 0.5002339610386185,
"gap_to_next": 4.919538083569819e-07,
"weight_pi_valley": 0.5000000003549374,
"dE": 0.00023396103861850204,
"T": -2.9175121706916417e-05,
"U_exp": 0.00026305535303938114,
"virial_2T": -5.8350243413832834e-05,
"virial_rUp": -5.732484761559691e-05,
"rms_size": 9.978858756269346,
"dE_deep_asym": 0.00022008782761320013,
"dE_shallow_asym": 0.008999999999999998,
"I1": 5.0,
"I2": -4.5,
"I_pair": 0.5030207717813825,
"D_num": 0.003020771781382159,
"D_formula": 0.0030133114299246686,
"D_general": 0.003012913668224544,
"D_deep_asym": 0.00040943181758237857,
"D_shallow_asym": 0.021290454514283685,
"rel_dev_D": 0.0024757983470950823,
"D_num_lin": 0.003002631253859356,
"dev_over_dE": 0.03188715309840583,
"dev_lin_over_dE": 0.04564937875287848,
"expected_scale": 0.0009638439020312571,
"T_over_dE": -0.12470077017605272,
"P": [
0.002,
0.004,
0.006
],
"E_b_P_num": [
0.5002379355735408,
0.5002498418991657,
0.5002696285469931
],
"E_b_P_formula": [
0.5002379370765375,
0.5002498651902945,
0.5002697453798893
],
"max_EP_dev_over_shift": 0.003275611377712108,
"quartic_coeff": -90.3157795464602,
"max_transfer_over_quantum": 0.053978943099708306,
"D_over_I": 0.006041543562764318,
"Omega_max": 4.000555516980667,
"decay_threshold": 2.0002777584903333,
"decay_margin": 2.9997222415096667,
"isolation_lhs": 9.933567294371953,
"lattice_over_dE": 11.223069315844745,
"strength": "deep",
"grip": "linear"
},
{
"r": 1.0,
"F1": 0.0009938079899999065,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
-1
],
"m_red": -45.0,
"E_b0": 0.5002339712299834,
"gap_to_next": 4.920612148850978e-07,
"weight_pi_valley": 0.5000000001293607,
"dE": 0.00023397122998336517,
"T": -2.9184079435092127e-05,
"U_exp": 0.000263064219034756,
"virial_2T": -5.8368158870184255e-05,
"virial_rUp": -5.731889368972418e-05,
"rms_size": 9.977584680572985,
"dE_deep_asym": 0.00022008782761320013,
"dE_shallow_asym": 0.008999999999999998,
"I1": 5.0,
"I2": -4.5,
"I_pair": 0.5028700326265805,
"D_num": 0.0028700326265802545,
"D_formula": 0.0028605383791416566,
"D_general": 0.0028593980235774954,
"D_deep_asym": 0.00023397122998336517,
"D_shallow_asym": 0.02129138192848623,
"rel_dev_D": 0.003319042145292518,
"D_num_lin": 0.002853652475163171,
"dev_over_dE": 0.04057869610410188,
"dev_lin_over_dE": 0.029430558530530726,
"expected_scale": 0.0009639909451313324,
"T_over_dE": -0.12473362403218144,
"P": [
0.002,
0.004,
0.006
],
"E_b_P_num": [
0.5002379469548576,
0.5002498568279294,
0.5002696493144555
],
"E_b_P_formula": [
0.5002379484758545,
0.5002498802134677,
0.5002697664428232
],
"max_EP_dev_over_shift": 0.0032829219787011,
"quartic_coeff": -90.43334484037489,
"max_transfer_over_quantum": 0.10795788619941661,
"D_over_I": 0.005740065253160509,
"Omega_max": 2.0002777584903333,
"decay_threshold": 1.0001388792451666,
"decay_margin": 3.9998611207548334,
"isolation_lhs": 9.96690063789665,
"lattice_over_dE": 11.226026162896328,
"strength": "deep",
"grip": "linear"
},
{
"r": 1.4,
"F1": 0.0007098628499999332,
"F2": 0.0,
"ell": 29.999999999999996,
"L": 1024,
"branches": [
1,
-1
],
"m_red": -45.0,
"E_b0": 0.5002339842896834,
"gap_to_next": 4.921991350048671e-07,
"weight_pi_valley": 0.4999999997378203,
"dE": 0.00023398428968335327,
"T": -2.9195569234543956e-05,
"U_exp": 0.0002630755843657716,
"virial_2T": -5.839113846908791e-05,
"virial_rUp": -5.731125999146994e-05,
"rms_size": 9.975951979851336,
"dE_deep_asym": 0.00022008782761320008,
"dE_shallow_asym": 0.008999999999999994,
"I1": 5.0,
"I2": -4.5,
"I_pair": 0.5026768710837499,
"D_num": 0.002676871083750143,
"D_formula": 0.0026649883491614524,
"D_general": 0.0026628676163632362,
"D_deep_asym": 9.359371587334192e-06,
"D_shallow_asym": 0.021292570361185148,
"rel_dev_D": 0.0044588317215081075,
"D_num_lin": 0.0026626161235334678,
"dev_over_dE": 0.05078432660915525,
"dev_lin_over_dE": 0.010138397031676584,
"expected_scale": 0.000964179448030513,
"T_over_dE": -0.1247757670998074,
"P": [
0.002,
0.004,
0.006
],
"E_b_P_num": [
0.5002379615404632,
0.5002498759627952,
0.5002696759378079
],
"E_b_P_formula": [
0.5002379630828087,
0.5002498994621848,
0.5002697934278115
],
"max_EP_dev_over_shift": 0.003291806621115322,
"quartic_coeff": -90.58263475722921,
"max_transfer_over_quantum": 0.15114104067918324,
"D_over_I": 0.005353742167500286,
"Omega_max": 1.428769827493095,
"decay_threshold": 0.7143849137465474,
"decay_margin": 4.285615086253452,
"isolation_lhs": 9.97642446048016,
"lattice_over_dE": 11.229819038982667,
"strength": "deep",
"grip": "linear"
},
{
"r": 0.5,
"F1": 0.00022084621999997922,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
-1
],
"m_red": -45.0,
"E_b0": 0.5000007501169758,
"gap_to_next": 8.101455062359264e-10,
"weight_pi_valley": 0.4999998475969507,
"dE": 7.501169757562209e-07,
"T": -4.435850307293477e-07,
"U_exp": 1.1936546083389013e-06,
"virial_2T": -8.871700614586954e-07,
"virial_rUp": -8.924890517969482e-07,
"rms_size": 93.35377579155704,
"dE_deep_asym": -1.932068253015259e-06,
"dE_shallow_asym": 1.3717421124828533e-06,
"I1": 5.0,
"I2": -4.5,
"I_pair": 0.5000409070753272,
"D_num": 4.090707532711235e-05,
"D_formula": 4.090266870016767e-05,
"D_general": 4.090391550099556e-05,
"D_deep_asym": 1.3127047075733866e-06,
"D_shallow_asym": 6.82606447938161e-05,
"rel_dev_D": 0.00010773446048190659,
"D_num_lin": 4.0903728823371566e-05,
"dev_over_dE": 0.005874586347336355,
"dev_lin_over_dE": 0.0014132771796392064,
"expected_scale": 7.166685715681208e-06,
"T_over_dE": -0.5913544754565154,
"P": [
0.002,
0.004,
0.006
],
"E_b_P_num": [
0.5000047483297382,
0.5000167254961688,
0.5000366295624702
],
"E_b_P_formula": [
0.5000047497897812,
0.5000167488081975,
0.5000367471722245
],
"max_EP_dev_over_shift": 0.003277914489704609,
"quartic_coeff": -91.31329180443959,
"max_transfer_over_quantum": 0.053978943099708306,
"D_over_I": 8.18141506542247e-05,
"Omega_max": 4.000555516980667,
"decay_threshold": 2.0002777584903333,
"decay_margin": 2.9997222415096667,
"isolation_lhs": 9.93333408345031,
"lattice_over_dE": 53.221902791086386,
"strength": "shallow",
"grip": "linear"
},
{
"r": 1.0,
"F1": 0.00011042310999998961,
"F2": 0.0,
"ell": 30.0,
"L": 1024,
"branches": [
1,
-1
],
"m_red": -45.0,
"E_b0": 0.5000007501179026,
"gap_to_next": 8.10148281793488e-10,
"weight_pi_valley": 0.500000007287332,
"dE": 7.501179025704019e-07,
"T": -4.435864139335199e-07,
"U_exp": 1.193655989950218e-06,
"virial_2T": -8.871728278670398e-07,
"virial_rUp": -8.924891442817578e-07,
"rms_size": 93.35370893228321,
"dE_deep_asym": -1.932068253015259e-06,
"dE_shallow_asym": 1.3717421124828533e-06,
"I1": 5.0,
"I2": -4.5,
"I_pair": 0.5000406823665311,
"D_num": 4.068236653154145e-05,
"D_formula": 4.0672895156587194e-05,
"D_general": 4.067816314644821e-05,
"D_deep_asym": 7.501179025704019e-07,
"D_shallow_asym": 6.826072913390657e-05,
"rel_dev_D": 0.00023286699699613564,
"D_num_lin": 4.067905669052907e-05,
"dev_over_dE": 0.012626515007571358,
"dev_lin_over_dE": 0.008214087306491258,
"expected_scale": 7.16669568585877e-06,
"T_over_dE": -0.5913555887861074,
"P": [
0.002,
0.004,
0.006
],
"E_b_P_num": [
0.5000047483324584,
0.5000167255042226,
0.5000366295792587
],
"E_b_P_formula": [
0.5000047497925458,
0.5000167488164758,
0.5000367471896923
],
"max_EP_dev_over_shift": 0.00327793197470377,
"quartic_coeff": -91.31353726780702,
"max_transfer_over_quantum": 0.10795788619941661,
"D_over_I": 8.13647330630829e-05,
"Omega_max": 2.0002777584903333,
"decay_threshold": 1.0001388792451666,
"decay_margin": 3.9998611207548334,
"isolation_lhs": 9.966667416784569,
"lattice_over_dE": 53.22200299074966,
"strength": "shallow",
"grip": "linear"
},
{
"r": 1.4,
"F1": 7.88736499999926e-05,
"F2": 0.0,
"ell": 29.999999999999996,
"L": 1024,
"branches": [
1,
-1
],
"m_red": -45.0,
"E_b0": 0.5000007501190887,
"gap_to_next": 8.101519455294692e-10,
"weight_pi_valley": 0.5000002339610143,
"dE": 7.501190887326814e-07,
"T": -4.435881846933018e-07,
"U_exp": 1.1936577586246076e-06,
"virial_2T": -8.871763693866036e-07,
"virial_rUp": -8.924892626636612e-07,
"rms_size": 93.35362332969032,
"dE_deep_asym": -1.932068253015259e-06,
"dE_shallow_asym": 1.3717421124828533e-06,
"I1": 5.0,
"I2": -4.5,
"I_pair": 0.5000403946524621,
"D_num": 4.0394652462083513e-05,
"D_formula": 4.037878604325204e-05,
"D_general": 4.038919733348302e-05,
"D_deep_asym": 3.000476354930745e-08,
"D_shallow_asym": 6.826083707467401e-05,
"rel_dev_D": 0.000392939471099485,
"D_num_lin": 4.039138926981156e-05,
"dev_over_dE": 0.021151866509997605,
"dev_lin_over_dE": 0.016801634232260425,
"expected_scale": 7.1667084501502055e-06,
"T_over_dE": -0.5913570143145398,
"P": [
0.002,
0.004,
0.006
],
"E_b_P_num": [
0.5000047483359408,
0.5000167255145324,
0.5000366296007518
],
"E_b_P_formula": [
0.5000047497960846,
0.5000167488270719,
0.5000367472120509
],
"max_EP_dev_over_shift": 0.0032779542427226883,
"quartic_coeff": -91.31386214296393,
"max_transfer_over_quantum": 0.15114104067918324,
"D_over_I": 8.078930492416703e-05,
"Omega_max": 1.428769827493095,
"decay_threshold": 0.7143849137465474,
"decay_margin": 4.285615086253452,
"isolation_lhs": 9.976191226309565,
"lattice_over_dE": 53.22213128830858,
"strength": "shallow",
"grip": "linear"
}
]
}output/mutual_term_check.json9 KB · raw
{
"max_rel_dev_all": 3.897751476969538e-14,
"cases": [
{
"case": {
"L": 16,
"kappa_h": 1.0,
"m_h": 0.3,
"tau": 0.8,
"M1": 0.7,
"M2": 0.5,
"F0": 1.0,
"F1": 0.3,
"F2": 0.2,
"sigma1": 1,
"sigma2": 1
},
"abar": 1.1044079964957103,
"eigvec_residual": 1.2401028427486198e-15,
"rows": [
{
"labels_n1_n2_m": [
0,
0,
1
],
"numerical": [
-0.009095531629472589,
-5.011369276867195e-17
],
"formula": -0.009095531629472589,
"rel_dev": 5.509704634117998e-15
},
{
"labels_n1_n2_m": [
1,
-2,
3
],
"numerical": [
-0.002055022405216982,
-3.7776884649305124e-19
],
"formula": -0.0020550224052169764,
"rel_dev": 2.7496018845798712e-15
},
{
"labels_n1_n2_m": [
3,
-5,
2
],
"numerical": [
-0.0019647772798085067,
1.4353025475214594e-17
],
"formula": -0.0019647772798085297,
"rel_dev": 1.3792099839515786e-14
},
{
"labels_n1_n2_m": [
-2,
4,
-1
],
"numerical": [
-0.00497183203244238,
-1.8622863212809886e-17
],
"formula": -0.004971832032442402,
"rel_dev": 5.7490609418608994e-15
},
{
"labels_n1_n2_m": [
5,
2,
7
],
"numerical": [
-0.0007791912219067409,
-2.31840925424854e-19
],
"formula": -0.0007791912219067381,
"rel_dev": 3.4913156748031588e-15
},
{
"labels_n1_n2_m": [
2,
2,
0
],
"numerical": [
-0.013263873307308011,
6.47154058509828e-35
],
"formula": -0.013263873307308263,
"rel_dev": 1.8963910329122623e-14
},
{
"labels_n1_n2_m": [
-3,
1,
0
],
"numerical": [
-0.014873993450272818,
-4.942551449792622e-35
],
"formula": -0.014873993450272793,
"rel_dev": 1.6327914050029304e-15
},
{
"labels_n1_n2_m": [
6,
-6,
8
],
"numerical": [
-0.0007598802139332297,
3.766671451786338e-19
],
"formula": -0.0007598802139332235,
"rel_dev": 8.290311254847195e-15
}
],
"max_rel_dev": 1.8963910329122623e-14
},
{
"case": {
"L": 16,
"kappa_h": 1.0,
"m_h": 0.3,
"tau": 0.8,
"M1": 0.7,
"M2": 0.5,
"F0": 1.0,
"F1": 0.3,
"F2": 0.0225,
"sigma1": 1,
"sigma2": 1
},
"abar": 1.0117458996057673,
"eigvec_residual": 1.2401028427486198e-15,
"rows": [
{
"labels_n1_n2_m": [
0,
0,
1
],
"numerical": [
-0.00786464976668061,
-4.3709330242262885e-17
],
"formula": -0.007864649766680611,
"rel_dev": 5.5620709887315565e-15
},
{
"labels_n1_n2_m": [
1,
-2,
3
],
"numerical": [
-0.0014901074050707327,
-1.7207426720664638e-19
],
"formula": -0.001490107405070737,
"rel_dev": 2.912690106592727e-15
},
{
"labels_n1_n2_m": [
3,
-5,
2
],
"numerical": [
-0.0014263056881132026,
1.013924362726558e-17
],
"formula": -0.0014263056881131915,
"rel_dev": 1.0519079363062898e-14
},
{
"labels_n1_n2_m": [
-2,
4,
-1
],
"numerical": [
-0.00401346513145179,
-1.494365719580665e-17
],
"formula": -0.004013465131451822,
"rel_dev": 8.820568839304457e-15
},
{
"labels_n1_n2_m": [
5,
2,
7
],
"numerical": [
-0.0004995978675767499,
3.733667855684837e-19
],
"formula": -0.0004995978675767546,
"rel_dev": 9.577859537479806e-15
},
{
"labels_n1_n2_m": [
2,
2,
0
],
"numerical": [
-0.011404426886681245,
2.337933810742404e-36
],
"formula": -0.011404426886681016,
"rel_dev": 2.0078474885604593e-14
},
{
"labels_n1_n2_m": [
-3,
1,
0
],
"numerical": [
-0.012960383691982028,
-3.6687004238147716e-36
],
"formula": -0.012960383691982028,
"rel_dev": 2.8307035586333926e-34
},
{
"labels_n1_n2_m": [
6,
-6,
8
],
"numerical": [
-0.0004848820280437704,
-1.301175741193455e-19
],
"formula": -0.00048488202804377825,
"rel_dev": 1.6213309975128075e-14
}
],
"max_rel_dev": 2.0078474885604593e-14
},
{
"case": {
"L": 16,
"kappa_h": 1.0,
"m_h": 0.3,
"tau": 0.8,
"M1": 0.7,
"M2": 0.5,
"F0": 1.0,
"F1": 0.3,
"F2": 0.2,
"sigma1": 1,
"sigma2": -1
},
"abar": 1.1044079964957103,
"eigvec_residual": 1.2401028427486198e-15,
"rows": [
{
"labels_n1_n2_m": [
0,
0,
1
],
"numerical": [
0.009095531629472586,
5.010945651449388e-17
],
"formula": 0.009095531629472589,
"rel_dev": 5.522428226449429e-15
},
{
"labels_n1_n2_m": [
1,
-2,
3
],
"numerical": [
0.0020550224052169807,
2.2527785353840697e-19
],
"formula": 0.0020550224052169764,
"rel_dev": 2.1131914798815703e-15
},
{
"labels_n1_n2_m": [
3,
-5,
2
],
"numerical": [
0.0019647772798085067,
-1.4431741308232534e-17
],
"formula": 0.0019647772798085297,
"rel_dev": 1.3813361791940207e-14
},
{
"labels_n1_n2_m": [
-2,
4,
-1
],
"numerical": [
0.004971832032442384,
1.8499102246367158e-17
],
"formula": 0.004971832032442402,
"rel_dev": 5.221673751335779e-15
},
{
"labels_n1_n2_m": [
5,
2,
7
],
"numerical": [
0.0007791912219067406,
9.53273701951327e-19
],
"formula": 0.0007791912219067381,
"rel_dev": 3.4261963570479904e-15
},
{
"labels_n1_n2_m": [
2,
2,
0
],
"numerical": [
0.013263873307308013,
-3.4407581456318445e-35
],
"formula": 0.013263873307308263,
"rel_dev": 1.8833124740645916e-14
},
{
"labels_n1_n2_m": [
-3,
1,
0
],
"numerical": [
0.01487399345027281,
7.665628986769642e-36
],
"formula": 0.014873993450272793,
"rel_dev": 1.1662795750020932e-15
},
{
"labels_n1_n2_m": [
6,
-6,
8
],
"numerical": [
0.0007598802139332297,
-4.082649082797704e-19
],
"formula": 0.0007598802139332235,
"rel_dev": 8.292901431948084e-15
}
],
"max_rel_dev": 1.8833124740645916e-14
},
{
"case": {
"L": 16,
"kappa_h": 1.0,
"m_h": 0.3,
"tau": 1.3,
"M1": 0.7,
"M2": 0.5,
"F0": 1.0,
"F1": 0.3,
"F2": 0.2,
"sigma1": 1,
"sigma2": 1
},
"abar": 1.1044079964957103,
"eigvec_residual": 1.898408963776082e-15,
"rows": [
{
"labels_n1_n2_m": [
0,
0,
1
],
"numerical": [
-0.009452768437474534,
-5.180710986354804e-17
],
"formula": -0.009452768437474474,
"rel_dev": 8.443487036947806e-15
},
{
"labels_n1_n2_m": [
1,
-2,
3
],
"numerical": [
-0.002154974744517884,
9.392057234842114e-20
],
"formula": -0.0021549747445178684,
"rel_dev": 7.245000815492042e-15
},
{
"labels_n1_n2_m": [
3,
-5,
2
],
"numerical": [
-0.0014044877488271026,
1.0317629824255665e-17
],
"formula": -0.0014044877488270796,
"rel_dev": 1.7938637053735863e-14
},
{
"labels_n1_n2_m": [
-2,
4,
-1
],
"numerical": [
-0.0035197995011773575,
-1.2775932186492922e-17
],
"formula": -0.0035197995011773432,
"rel_dev": 5.45043427745903e-15
},
{
"labels_n1_n2_m": [
5,
2,
7
],
"numerical": [
-0.0007897085393569411,
-1.8911538743628514e-17
],
"formula": -0.0007897085393569168,
"rel_dev": 3.897751476969538e-14
},
{
"labels_n1_n2_m": [
2,
2,
0
],
"numerical": [
-0.0077984672498935224,
2.8061683132107806e-35
],
"formula": -0.007798467249893521,
"rel_dev": 2.22444157343931e-16
},
{
"labels_n1_n2_m": [
-3,
1,
0
],
"numerical": [
-0.00946145479080685,
6.923458992192756e-35
],
"formula": -0.009461454790806904,
"rel_dev": 5.683737749033285e-15
},
{
"labels_n1_n2_m": [
6,
-6,
8
],
"numerical": [
-0.0007598802139332206,
3.041983685234327e-19
],
"formula": -0.0007598802139332235,
"rel_dev": 3.7312349346042454e-15
}
],
"max_rel_dev": 3.897751476969538e-14
}
]
}output/run_bound_pair.log7 KB · raw
+1+1 deep square r=0.50 size=10.0 dE=-4.445e-03 T/dE=-0.125 D_num=4.2556e-02 D_lin=4.2366e-02 D_form=4.2510e-02 D_gen=4.2517e-02 dev/dE=0.010 devlin/dE=0.032 scale=0.001 D/I=0.004 EPdev=0.016 ratio=0.05 gap=9.34e-06 wpi=0.50 margin=0.499 isol=18.929 latt/dE=-11.220 t=77s
+1+1 deep square r=1.00 size=10.0 dE=-4.445e-03 T/dE=-0.125 D_num=4.5447e-02 D_lin=4.5230e-02 D_form=4.5443e-02 D_gen=4.5464e-02 dev/dE=0.001 devlin/dE=0.048 scale=0.001 D/I=0.005 EPdev=0.016 ratio=0.11 gap=9.35e-06 wpi=0.50 margin=2.500 isol=18.962 latt/dE=-11.223 t=155s
+1+1 deep square r=1.40 size=10.0 dE=-4.446e-03 T/dE=-0.125 D_num=4.9154e-02 D_lin=4.8901e-02 D_form=4.9197e-02 D_gen=4.9237e-02 dev/dE=0.010 devlin/dE=0.067 scale=0.001 D/I=0.005 EPdev=0.016 ratio=0.15 gap=9.35e-06 wpi=0.50 margin=3.071 isol=18.972 latt/dE=-11.226 t=229s
+1+1 shallow square r=0.50 size=93.4 dE=-1.425e-05 T/dE=-0.591 D_num=7.4049e-04 D_lin=7.4043e-04 D_form=7.3990e-04 D_gen=7.3987e-04 dev/dE=0.041 devlin/dE=0.037 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.05 gap=1.54e-08 wpi=0.50 margin=0.499 isol=18.933 latt/dE=-53.221 t=301s
+1+1 shallow square r=1.00 size=93.4 dE=-1.425e-05 T/dE=-0.591 D_num=7.4476e-04 D_lin=7.4470e-04 D_form=7.4427e-04 D_gen=7.4417e-04 dev/dE=0.035 devlin/dE=0.030 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.11 gap=1.54e-08 wpi=0.50 margin=2.500 isol=18.967 latt/dE=-53.221 t=373s
+1+1 shallow square r=1.40 size=93.4 dE=-1.425e-05 T/dE=-0.591 D_num=7.5023e-04 D_lin=7.5017e-04 D_form=7.4986e-04 D_gen=7.4966e-04 dev/dE=0.026 devlin/dE=0.022 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.15 gap=1.54e-08 wpi=0.50 margin=3.071 isol=18.976 latt/dE=-53.222 t=446s
+1+1 v-shallow square r=0.50 size=70.5 dE=-2.192e-05 T/dE=-0.809 D_num=1.5712e-03 D_lin=1.5710e-03 D_form=1.5708e-03 D_gen=1.5709e-03 dev/dE=0.019 devlin/dE=0.007 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.05 gap=3.30e-07 wpi=0.50 margin=0.492 isol=18.750 latt/dE=-72.808 t=520s
+1+1 v-shallow square r=1.00 size=70.5 dE=-2.192e-05 T/dE=-0.809 D_num=1.5743e-03 D_lin=1.5741e-03 D_form=1.5740e-03 D_gen=1.5744e-03 dev/dE=0.017 devlin/dE=0.005 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.10 gap=3.30e-07 wpi=0.50 margin=2.496 isol=18.875 latt/dE=-72.809 t=595s
+1+1 v-shallow square r=1.40 size=70.5 dE=-2.192e-05 T/dE=-0.809 D_num=1.5783e-03 D_lin=1.5781e-03 D_form=1.5780e-03 D_gen=1.5787e-03 dev/dE=0.014 devlin/dE=0.002 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.14 gap=3.31e-07 wpi=0.50 margin=3.069 isol=18.911 latt/dE=-72.809 t=671s
+1+1 deep linear r=0.50 size=10.0 dE=-4.445e-03 T/dE=-0.125 D_num=4.2555e-02 D_lin=4.2366e-02 D_form=4.2509e-02 D_gen=4.2516e-02 dev/dE=0.010 devlin/dE=0.032 scale=0.001 D/I=0.004 EPdev=0.016 ratio=0.05 gap=9.34e-06 wpi=0.50 margin=2.500 isol=18.929 latt/dE=-11.220 t=672s
+1+1 deep linear r=1.00 size=10.0 dE=-4.445e-03 T/dE=-0.125 D_num=4.5446e-02 D_lin=4.5230e-02 D_form=4.5442e-02 D_gen=4.5463e-02 dev/dE=0.001 devlin/dE=0.048 scale=0.001 D/I=0.005 EPdev=0.016 ratio=0.11 gap=9.35e-06 wpi=0.50 margin=3.500 isol=18.962 latt/dE=-11.223 t=675s
+1+1 deep linear r=1.40 size=10.0 dE=-4.446e-03 T/dE=-0.125 D_num=4.9153e-02 D_lin=4.8900e-02 D_form=4.9197e-02 D_gen=4.9237e-02 dev/dE=0.010 devlin/dE=0.067 scale=0.001 D/I=0.005 EPdev=0.016 ratio=0.15 gap=9.35e-06 wpi=0.50 margin=3.786 isol=18.972 latt/dE=-11.226 t=676s
+1+1 shallow linear r=0.50 size=93.4 dE=-1.425e-05 T/dE=-0.591 D_num=7.4049e-04 D_lin=7.4043e-04 D_form=7.3990e-04 D_gen=7.3987e-04 dev/dE=0.041 devlin/dE=0.037 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.05 gap=1.54e-08 wpi=0.50 margin=2.500 isol=18.933 latt/dE=-53.221 t=678s
+1+1 shallow linear r=1.00 size=93.4 dE=-1.425e-05 T/dE=-0.591 D_num=7.4476e-04 D_lin=7.4470e-04 D_form=7.4427e-04 D_gen=7.4417e-04 dev/dE=0.035 devlin/dE=0.030 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.11 gap=1.54e-08 wpi=0.50 margin=3.500 isol=18.967 latt/dE=-53.221 t=680s
+1+1 shallow linear r=1.40 size=93.4 dE=-1.425e-05 T/dE=-0.591 D_num=7.5023e-04 D_lin=7.5017e-04 D_form=7.4986e-04 D_gen=7.4966e-04 dev/dE=0.026 devlin/dE=0.022 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.15 gap=1.54e-08 wpi=0.50 margin=3.786 isol=18.976 latt/dE=-53.222 t=681s
+1+1 v-shallow linear r=0.50 size=70.5 dE=-2.192e-05 T/dE=-0.809 D_num=1.5712e-03 D_lin=1.5710e-03 D_form=1.5708e-03 D_gen=1.5709e-03 dev/dE=0.019 devlin/dE=0.007 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.05 gap=3.30e-07 wpi=0.50 margin=2.496 isol=18.750 latt/dE=-72.808 t=683s
+1+1 v-shallow linear r=1.00 size=70.5 dE=-2.192e-05 T/dE=-0.809 D_num=1.5743e-03 D_lin=1.5741e-03 D_form=1.5740e-03 D_gen=1.5743e-03 dev/dE=0.017 devlin/dE=0.005 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.10 gap=3.30e-07 wpi=0.50 margin=3.498 isol=18.875 latt/dE=-72.809 t=686s
+1+1 v-shallow linear r=1.40 size=70.5 dE=-2.192e-05 T/dE=-0.809 D_num=1.5783e-03 D_lin=1.5781e-03 D_form=1.5780e-03 D_gen=1.5787e-03 dev/dE=0.014 devlin/dE=0.002 scale=0.000 D/I=0.000 EPdev=0.016 ratio=0.14 gap=3.31e-07 wpi=0.50 margin=3.784 isol=18.911 latt/dE=-72.809 t=687s
+1-1 deep linear r=0.50 size=10.0 dE=2.340e-04 T/dE=-0.125 D_num=3.0208e-03 D_lin=3.0026e-03 D_form=3.0133e-03 D_gen=3.0129e-03 dev/dE=0.032 devlin/dE=0.046 scale=0.001 D/I=0.006 EPdev=0.003 ratio=0.05 gap=4.92e-07 wpi=0.50 margin=3.000 isol=9.934 latt/dE=11.223 t=689s
+1-1 deep linear r=1.00 size=10.0 dE=2.340e-04 T/dE=-0.125 D_num=2.8700e-03 D_lin=2.8537e-03 D_form=2.8605e-03 D_gen=2.8594e-03 dev/dE=0.041 devlin/dE=0.029 scale=0.001 D/I=0.006 EPdev=0.003 ratio=0.11 gap=4.92e-07 wpi=0.50 margin=4.000 isol=9.967 latt/dE=11.226 t=691s
+1-1 deep linear r=1.40 size=10.0 dE=2.340e-04 T/dE=-0.125 D_num=2.6769e-03 D_lin=2.6626e-03 D_form=2.6650e-03 D_gen=2.6629e-03 dev/dE=0.051 devlin/dE=0.010 scale=0.001 D/I=0.005 EPdev=0.003 ratio=0.15 gap=4.92e-07 wpi=0.50 margin=4.286 isol=9.976 latt/dE=11.230 t=693s
+1-1 shallow linear r=0.50 size=93.4 dE=7.501e-07 T/dE=-0.591 D_num=4.0907e-05 D_lin=4.0904e-05 D_form=4.0903e-05 D_gen=4.0904e-05 dev/dE=0.006 devlin/dE=0.001 scale=0.000 D/I=0.000 EPdev=0.003 ratio=0.05 gap=8.10e-10 wpi=0.50 margin=3.000 isol=9.933 latt/dE=53.222 t=695s
+1-1 shallow linear r=1.00 size=93.4 dE=7.501e-07 T/dE=-0.591 D_num=4.0682e-05 D_lin=4.0679e-05 D_form=4.0673e-05 D_gen=4.0678e-05 dev/dE=0.013 devlin/dE=0.008 scale=0.000 D/I=0.000 EPdev=0.003 ratio=0.11 gap=8.10e-10 wpi=0.50 margin=4.000 isol=9.967 latt/dE=53.222 t=697s
+1-1 shallow linear r=1.40 size=93.4 dE=7.501e-07 T/dE=-0.591 D_num=4.0395e-05 D_lin=4.0391e-05 D_form=4.0379e-05 D_gen=4.0389e-05 dev/dE=0.021 devlin/dE=0.017 scale=0.000 D/I=0.000 EPdev=0.003 ratio=0.15 gap=8.10e-10 wpi=0.50 margin=4.286 isol=9.976 latt/dE=53.222 t=698s
max dev/dE: 0.05078432660915525 max devlin/dE: 0.06679796736019555
output/run_mutual_term.log333 B · raw
0.8 0.2 1 max rel dev 1.8963910329122623e-14 resid 1.2401028427486198e-15
0.8 0.0225 1 max rel dev 2.0078474885604593e-14 resid 1.2401028427486198e-15
0.8 0.2 -1 max rel dev 1.8833124740645916e-14 resid 1.2401028427486198e-15
1.3 0.2 1 max rel dev 3.897751476969538e-14 resid 1.898408963776082e-15
overall 3.897751476969538e-14
nDot Physics Research