def Edis(pair):
q1 = np.sum(pair[0] * xpGrid[:, 0])
p1 = np.sum(pair[0] * xpGrid[:, 1])
q2 = np.sum(pair[1] * xpGrid[:, 0])
p2 = np.sum(pair[1] * xpGrid[:, 1])
return qkr.dist(([q1, p1], [q2, p2]))
ax = np.arange(0.,m)*dq
Qs = np.tile(np.arange(0,m)*dq,(m,1)).T
Ps = np.tile(np.arange(0,m)*dp,(m,1))
xpGrid = np.array([[ax[i],ax[j]] for i in range(m) for j in range(m)])
hamil = np.sum([blc(j) for j in np.arange(-int(3.*k/np.pi),1 + int(3.*k/np.pi))], axis=0)
eigs = np.linalg.eig(hamil)
eigVal = eigs[0]
eigVec = eigs[1]
disMat = np.zeros((m**2,m**2))
for i in range(m**2):
for j in range(m**2):
disMat[i,j] = qkr.dist((xpGrid[i], xpGrid[j]))
pool = mp.Pool(mp.cpu_count())
eigProbs = np.array(pool.map(phi2Ph, eigVec))
pool.close()
np.save(foldPref+"/hamil.npy",hamil)
np.savetxt(foldPref+"/disMat.dat",disMat)
np.save(foldPref+"/eigs.npy", eigVal)
np.save(foldPref+"/eigv.npy", eigVec)
np.savetxt(foldPref+"/xpGrid.dat", xpGrid)
np.save(foldPref+"/eigPrb.npy", eigProbs)
except FileExistsError:
eigVal = np.load(foldPref+"/eigs.npy")
qlis = np.array([[ini[0, 0], ini[1, 0]]])
plis = np.array([[ini[0, 1], ini[1, 1]]])
trajLen = 50
"""
Classical Evolution
"""
for ki in range(trajLen):
plis = np.concatenate(
(plis, [np.mod(plis[-1] + k * np.sin(qlis[-1]), 2. * np.pi)]))
qlis = np.concatenate((qlis, [np.mod(qlis[-1] + plis[-1], 2. * np.pi)]))
st1 = np.transpose([qlis[:, 0], plis[:, 0]])
st2 = np.transpose([qlis[:, 1], plis[:, 1]])
clis = [qkr.dist((s1, s2)) for s1, s2 in zip(st1, st2)]
"""
Quantal Evolution
"""
def blc(l):
bone = np.array(range(m**2))
indMat = (bone + l * m**2) - np.transpose([bone])
sign = (np.complex(0, -1))**indMat
jvs = sp.jv(indMat, k / hbar)
phs = np.exp(np.complex(0, -1) * bone**2 * hbar / 2.)
return np.multiply(np.multiply(sign, jvs), phs)
def phi2Ph(phi):