def findPhotonNumberInGS2nd(etas):
photonNumber = np.zeros((len(etas)), dtype='double')
for indEta in np.arange(len(etas)):
gsTemp = findGS(etas[indEta])
print("J(GS) = {}".format(eF.J(gsTemp[0:-1])))
phNum = sec_order.photonNumber.avPhotonNumber2nd(gsTemp, etas[indEta])
photonNumber[indEta] = phNum
return photonNumber
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 anaGreenVecTLesser(kVec, tVec, eta, damping):
gs = anaGS.findGS1st(eta)
gsJ = eF.J(gs[0: -1])
_, occupations = np.meshgrid(np.ones(tVec.shape), gs[0: -1])
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 avPhotonNumber2nd(state, eta):
#return avPhotonNumber1st(state, eta)
assert (len(state) == param.chainLength + 1)
assert (np.abs(state[-1]) < 1e-10)
#gam = eF.gamma(state[0: -1], eta)
gsT = param.t / (np.pi) * (np.sin(np.pi / 2.) -
np.sin(-np.pi / 2.)) * param.chainLength
gsJ = param.t / (np.pi) * (np.cos(np.pi / 2.) -
np.cos(-np.pi / 2.)) * param.chainLength
gsT = eF.T(state[:-1])
gsJ = eF.J(state[:-1])
gam = eta**2 * gsT / (eta**2 * gsT - param.w0)
epsilon = np.sqrt(1. - gam**2)
u = eF.calcU(gam)
v = eF.calcV(gam)
vsq = np.abs(v)**2
upvsq = np.abs(u + v)**2
X = eta * eF.J(state[0:-1]) / (2. * epsilon * eF.LT(state[0:-1], eta))
return vsq + X**2 * upvsq
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 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 avPhotonNumber1st(state, eta):
assert (len(state) == param.chainLength + 1)
assert (np.abs(state[-1]) < 1e-10)
return (eta * eF.J(state[0:-1]) / param.w0)**2
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)
def avPhotonNum(electronicState, eta, orderH):
T = eF.T(electronicState)
J = eF.J(electronicState)
av = averagePhotonNumber([T, J], eta, orderH)
return av
def photonGS(electronicState, eta, orderH):
T = eF.T(electronicState)
J = eF.J(electronicState)
gs = findPhotonGS([T, J], eta, orderH)
return gs
def energyFromState(electronicState, eta, orderH):
T = eF.T(electronicState)
J = eF.J(electronicState)
E = findSmalestEigenvalue([T, J], eta, orderH)
return E
