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https://github.com/vale981/hopsflow
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something's afoot for asymmetric baths
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1 changed files with 83 additions and 69 deletions
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@ -10,9 +10,9 @@ from .util import BCF
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import numpy as np
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from numpy.typing import NDArray
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from numpy.polynomial import Polynomial
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from typing import Generator, Union, Optional
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from typing import Union, Optional
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from itertools import product
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from collections.abc import Iterator
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from collections.abc import Iterator, Callable
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@dataclass
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@ -273,8 +273,8 @@ class CorrelationMatrix(Propagator):
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):
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super().__init__(sys)
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self.G = self._residual_matrix
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self.G_e = -self._roots
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self.G = self._residual_matrix.copy()
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self.G_e = -self._roots.copy()
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α = []
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αe = []
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@ -286,14 +286,14 @@ class CorrelationMatrix(Propagator):
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α[i] *= scale
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else:
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α.append(self.params.G[i])
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αe.append(self.params.W[i])
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α.append(self.params.G[i].copy())
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αe.append(self.params.W[i].copy())
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self.αc = np.array(list(map(np.conj, α)), dtype=object)
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self.αce = np.array(list(map(np.conj, αe)), dtype=object)
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self.α = np.array(α, dtype=object)
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self.αe = np.array(αe, dtype=object)
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self.initial_corr = initial_corr
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self.initial_corr = initial_corr.copy()
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def __call__(
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self,
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@ -375,61 +375,62 @@ class CorrelationMatrix(Propagator):
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/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
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)
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else:
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for i, j, m, n, g in iterate_ragged(
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G.shape[0],
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G.shape[0],
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G_e.shape[0],
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G_e.shape[0],
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len(α[l]),
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):
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for l in range(len(α)):
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for i, j, m, n, g in iterate_ragged(
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G.shape[0],
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G.shape[0],
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G_e.shape[0],
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G_e.shape[0],
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len(α[l]),
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):
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result[:, i, j] += (
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-(
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(
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np.exp(-(s * G_e[n]) - t * α_e[l][g])
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result[:, i, j] += (
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-(
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(
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np.exp(-(s * G_e[n]) - t * α_e[l][g])
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* G[i, 1 + 2 * l, m]
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* G[j, 1 + 2 * l, n]
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* α[l][g]
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)
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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)
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+ (
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np.exp(s * α_e[l][g] - t * α_e[l][g])
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* G[i, 1 + 2 * l, m]
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* G[j, 1 + 2 * l, n]
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* α[l][g]
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)
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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)
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+ (
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np.exp(s * α_e[l][g] - t * α_e[l][g])
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* G[i, 1 + 2 * l, m]
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* G[j, 1 + 2 * l, n]
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* α[l][g]
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)
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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+ np.exp(-(t * G_e[m]) - s * G_e[n])
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* (
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-(
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+ np.exp(-(t * G_e[m]) - s * G_e[n])
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* (
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-(
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(G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] + α_e[l][g]))
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)
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+ (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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+ (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * αc[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] - αc_e[l][g]))
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)
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- (
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np.exp(-(t * G_e[m]) - s * αc_e[l][g])
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* G[i, 1 + 2 * l, m]
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* G[j, 1 + 2 * l, n]
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* αc[l][g]
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)
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/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
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+ np.exp(s * G_e[m] - t * G_e[m])
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* (
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(G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] + α_e[l][g]))
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- (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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- (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * αc[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] - αc_e[l][g]))
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+ (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * αc[l][g])
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/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
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)
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+ (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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+ (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * αc[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] - αc_e[l][g]))
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)
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- (
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np.exp(-(t * G_e[m]) - s * αc_e[l][g])
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* G[i, 1 + 2 * l, m]
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* G[j, 1 + 2 * l, n]
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* αc[l][g]
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)
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/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
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+ np.exp(s * G_e[m] - t * G_e[m])
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* (
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(G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] + α_e[l][g]))
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- (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * α[l][g])
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/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
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- (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * αc[l][g])
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/ ((G_e[m] + G_e[n]) * (G_e[n] - αc_e[l][g]))
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+ (G[i, 1 + 2 * l, m] * G[j, 1 + 2 * l, n] * αc[l][g])
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/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
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)
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)
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return result
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@ -452,7 +453,9 @@ class CorrelationMatrix(Propagator):
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)
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) - 1 / 2 * γ * np.real(correlation_matrix[:, 0, 2])
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def Q1(self, t: np.ndarray, u: int) -> NDArray[np.complex128]:
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def Q1(
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self, t: np.ndarray, u: int, exp: Callable[[np.ndarray], np.ndarray] = np.exp
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) -> NDArray[np.complex128]:
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G = self.G
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G_e = self.G_e
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@ -466,19 +469,21 @@ class CorrelationMatrix(Propagator):
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):
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result += (
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(
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(np.exp(t * G_e[h]) - np.exp(t * α0d_e[m]))
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(exp(t * G_e[h]) - exp(t * α0d_e[m]))
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* G[2 * u, j, h]
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* G[2 * u, k, l]
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* ic[k, j]
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* α0d[m]
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)
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* np.exp(-t * (G_e[h] + G_e[l] + α0d_e[m]))
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* exp(-t * (G_e[h] + G_e[l] + α0d_e[m]))
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/ ((G_e[h] - α0d_e[m]))
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)
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return result
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def Q2(self, t: np.ndarray, u: int) -> NDArray[np.complex128]:
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def Q2(
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self, t: np.ndarray, u: int, exp: Callable[[np.ndarray], np.ndarray] = np.exp
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) -> NDArray[np.complex128]:
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G = self.G
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G_e = self.G_e
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@ -512,7 +517,7 @@ class CorrelationMatrix(Propagator):
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* α0d[r]
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* α[l][g]
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)
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* np.exp(-t * (G_e[n] + α_e[l][g]))
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* exp(-t * (G_e[n] + α_e[l][g]))
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/ (
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(-G_e[n] + α0d_e[r])
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* (G_e[m] - α_e[l][g])
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@ -553,7 +558,7 @@ class CorrelationMatrix(Propagator):
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* (α0d_e[r] + α_e[l][g])
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)
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)
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* np.exp(-t * (α0d_e[r] + α_e[l][g]))
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* exp(-t * (α0d_e[r] + α_e[l][g]))
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+ (
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-(
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(
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@ -591,7 +596,7 @@ class CorrelationMatrix(Propagator):
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* (G_e[n] - αc_e[l][g])
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)
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)
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* np.exp(-t * (G_e[m] + G_e[n]))
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* exp(-t * (G_e[m] + G_e[n]))
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- (
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G[2 * u, 1 + 2 * l, m]
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* G[2 * u, 1 + 2 * l, n]
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@ -616,7 +621,7 @@ class CorrelationMatrix(Propagator):
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* α0d[r]
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* αc[l][g]
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)
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* np.exp(-t * (G_e[m] + αc_e[l][g]))
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* exp(-t * (G_e[m] + αc_e[l][g]))
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/ (
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(G_e[n] - αc_e[l][g])
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* (α0d_e[r] - αc_e[l][g])
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@ -714,12 +719,14 @@ class CorrelationMatrix(Propagator):
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* (G_e[m] + αc_e[l][g])
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)
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)
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* np.exp(-t * (G_e[m] + α0d_e[r]))
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* exp(-t * (G_e[m] + α0d_e[r]))
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)
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return result
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def Q3(self, t: np.ndarray, u: int) -> NDArray[np.complex128]:
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def Q3(
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self, t: np.ndarray, u: int, exp: Callable[[np.ndarray], np.ndarray] = np.exp
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) -> NDArray[np.complex128]:
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G = self.G
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G_e = self.G_e
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@ -732,23 +739,22 @@ class CorrelationMatrix(Propagator):
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)
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result = np.zeros_like(t, dtype=np.complex128)
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for k, i in iterate_ragged(len(α0d), len(G_e)):
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for k, i in iterate_ragged(len(αd), len(G_e)):
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for j in range(len(αd[k])):
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result += -(
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(G[2 * u, 1 + 2 * k, i] * αd[k][j]) / (-G_e[i] - αd_e[k][j])
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) + (
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np.exp(-(t * G_e[i]) - t * αd_e[k][j])
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* G[2 * u, 1 + 2 * k, i]
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* αd[k][j]
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exp(-t * (G_e[i] + αd_e[k][j])) * G[2 * u, 1 + 2 * k, i] * αd[k][j]
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) / (
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-G_e[i] - αd_e[k][j]
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)
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for k, i in iterate_ragged(len(α0d), len(G_e)):
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for l in range(len(α0d[k])):
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result += (G[2 * u, 1 + 2 * k, i] * α0d[k][l]) / (
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-G_e[i] - α0d_e[k][l]
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) - (
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np.exp(-(t * G_e[i]) - t * α0d_e[k][l])
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exp(-t * (G_e[i] + α0d_e[k][l]))
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* G[2 * u, 1 + 2 * k, i]
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* α0d[k][l]
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) / (
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@ -757,8 +763,16 @@ class CorrelationMatrix(Propagator):
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return result
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def flow(self, t: np.ndarray, u: int) -> NDArray[np.float64]:
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return 1 / 2 * (np.real(self.Q3(t, u)) - np.imag(self.Q1(t, u) + self.Q2(t, u)))
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def flow(self, t: np.ndarray, u: int, steady: bool = False) -> NDArray[np.float64]:
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exp = np.zeros_like if steady else np.exp
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return (
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1
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/ 2
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* (
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np.real(self.Q3(t, u, exp))
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- np.imag(self.Q1(t, u, exp) + self.Q2(t, u, exp))
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)
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)
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def initial_correlation_pure_osci(n: int, m: int):
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