def nonEqGFParametersAboveFS(nCoh, kPoint, wVec, damping):
if (nCoh == 0):
eta = 2.5 / np.sqrt(prms.chainLength)
else:
eta = np.sqrt(0.4 / nCoh) / np.sqrt(prms.chainLength)
print("nCoh = {} ; eta = {}".format(nCoh, eta * np.sqrt(prms.chainLength)))
gs = arbOrder.findGS(eta, 3)
gsT = eF.T(gs)
wTilde = np.sqrt(1. - 2. * eta**2 / prms.w0 * gsT)
tau = 2. * np.pi / wTilde
tauLength = 1.
tAv = np.linspace(1000. * tau, (1000. + tauLength) * tau,
20,
endpoint=False)
gfNonEq = nonEqGreenPoint.gfCohW(kPoint=kPoint,
wRel=wVec,
tAv=tAv,
eta=eta,
damping=damping,
N=nCoh)
gfNonEqN0 = 1. / (tauLength * tau) * (tAv[1] - tAv[0]) * np.sum(gfNonEq,
axis=1)
return gfNonEqN0
def getPhGS(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
gsJ = 0.
gsT = -2. / np.pi * prms.chainLength
return phState.findPhotonGS([gsT, gsJ], eta, 3)
def expectAnnihil(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
ptGS = phState.findPhotonGS([gsT, gsJ], eta, 3)
a = setUpAnnihil(eta)
return np.dot(np.conj(ptGS), np.dot(a, ptGS))
def currentGS(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
ptGS = phState.findPhotonGS([gsT, gsJ], eta, 3)
jOp = setupCurrentOperator(gsT, gsJ, eta)
current = np.dot(np.conj(ptGS), np.dot(jOp, ptGS))
return current
def expectSinA(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
ptGS = phState.findPhotonGS([gsT, gsJ], eta, 3)
x = setUpA(eta)
sinX = sciLin.sinm(x)
return np.dot(np.conj(ptGS), np.dot(sinX, ptGS))
def gfNumVecTGreater(kVec, tVec, eta, damping):
gs = arbOrder.findGS(eta, 1)
_, occupations = np.meshgrid(np.ones(tVec.shape), gs[:])
GF = gfNumPointTGreater(kVec, tVec, eta)
GF = np.multiply(1 - occupations, GF)
dampingArr, _ = np.meshgrid(np.exp(-damping * np.abs(tVec)),
np.ones(kVec.shape))
GF = np.multiply(dampingArr, GF)
return GF
def gfNumVecTGreater(kVec, tVec, eta, damping):
if (len(kVec) == prms.chainLength):
gs = arbOrder.findGS(eta, 3)
else:
gs = np.ones(len(kVec), dtype=complex)
_, occupations = np.meshgrid(np.ones(tVec.shape), gs[:])
GF = gfNumPointTGreater(kVec, tVec, eta)
GF = np.multiply(1 - occupations, GF)
dampingArr, _ = np.meshgrid(np.exp(-damping * np.abs(tVec)),
np.ones(kVec.shape))
GF = np.multiply(dampingArr, GF)
return GF
def anaGreenVecTLesser(kVec, tVec, eta, damping):
if (len(kVec) == prms.chainLength):
gs = arbOrder.findGS(eta, 3)
else:
gs = np.ones(kVec.shape, dtype=complex)
_, occupations = np.meshgrid(np.ones(tVec.shape), gs[:])
gsJ = 0.
GF = anaGreenPointTLesser(kVec, tVec, gsJ, eta)
GF = np.multiply(occupations, GF)
dampingArr, _ = np.meshgrid(np.exp(-damping * np.abs(tVec)),
np.ones(kVec.shape))
GF = np.multiply(dampingArr, GF)
return GF
def anaGreenVecT(kVec, tVec, eta, damping):
if (len(kVec) == prms.chainLength):
gs = arbOrder.findGS(eta, 3)
else: #don't include occupations if length of kVec doesnt match chain length
gs = np.ones(len(kVec), dtype=complex)
_, occupations = np.meshgrid(np.ones(tVec.shape), gs[:])
gsJ = 0.
GF = anaGreenPointT(kVec, tVec, gsJ, eta)
GF = np.multiply(1 - occupations, GF)
dampingArr, _ = np.meshgrid(np.exp(-damping * np.abs(tVec)),
np.ones(kVec.shape))
GF = np.multiply(dampingArr, GF)
return GF
def anaGreenVecTGreater(kVec, tVec, eta, damping):
#gs = anaGS.findGS1st(eta)
#gsJ = eF.J(gs[0: -1])
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
_, occupations = np.meshgrid(np.ones(tVec.shape), gs)
GF = anaGreenPointTGreater(kVec, tVec, gsJ, eta)
GF = np.multiply(1 - occupations, GF)
dampingArr, _ = np.meshgrid(np.exp(- damping * np.abs(tVec)), np.ones(kVec.shape))
GF = np.multiply(dampingArr, GF)
return GF
def electronicGSMatches1st():
eta = 1. / np.sqrt(prms.chainLength)
gsAna = analytical.findGS1st(eta)
gsAna = gsAna[:-1]
gsNum = numerical.findGS(eta, 1)
failArr = (np.abs(gsAna - gsNum) > 1e-8)
#print("gsAna = {}".format(gsAna))
#print("gsNum = {}".format(gsNum))
if (np.any(failArr)):
print(" Numerical and Analytical result differ for GS 1st!!! ------ CHECK FAILED!!!")
return False
else:
print(" Numerical and Analytical result consistent for GS 1st! ------ CHECK PASSED :)")
return True
def anaGreenPointTLesser(kPoint, tPoint, gsJ, eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
#gsT = - 2. / np.pi * prms.chainLength
z = 2. * eta**2 / prms.w0 * gsT
wTilde = prms.w0 * np.sqrt(1. - z)
epsK = 2. * prms.t * np.cos(
kPoint[:, None]) * (1. - 0.5 * eta**2 * prms.w0 / wTilde)
selfE = eta**2 * prms.w0 / (wTilde**2) * (-2. * prms.t *
np.sin(kPoint[:, None]))**2
eTime = -1j * epsK * tPoint[None, :] - 1j * selfE * tPoint[None, :]
ptTime = -(-2. * eta * prms.t * np.sin(kPoint[:, None]))**2 * prms.w0 / (
wTilde**3) * (1. - np.exp(1j * wTilde * tPoint[None, :]))
return -1j * np.exp(eTime + ptTime)
def getH(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
return numH.setupPhotonHamiltonianInf(gsT, gsJ, eta)
def getPhGS(eta):
gs = arbOrder.findGS(eta, 3)
gsJ = eF.J(gs)
gsT = eF.T(gs)
return phState.findPhotonGS([gsT, gsJ], eta, 3)
