def merge_normal_distributions(self, fill=0):
"""Merge all normal distributed rvs together into one joint normal
Set new covariances (and previous 0 covs) to 'fill'
"""
non_altered = []
means = []
blocks = []
names = []
for rvs, dist in self.distributions():
names.extend([rv.name for rv in rvs])
if isinstance(dist, stats.crv_types.NormalDistribution):
means.append(dist.mean)
blocks.append(sympy.Matrix([dist.std**2]))
elif isinstance(dist, stats.joint_rv_types.MultivariateNormalDistribution):
means.extend(dist.mu)
blocks.append(dist.sigma)
else:
non_altered.extend(rvs)
if names:
if len(blocks) > 1:
# Need special case for len(blocks) == 1 because of sympy 1.5.1 bug #18618
M = sympy.BlockDiagMatrix(*blocks)
M = sympy.Matrix(M)
else:
M = sympy.Matrix(blocks[0])
if fill != 0:
for row, col in itertools.product(range(M.rows), range(M.cols)):
if M[row, col] == 0:
M[row, col] = fill
new_rvs = JointNormalSeparate(names, means, M)
self.__init__(new_rvs + non_altered)
def make_syst(a, width):
kx, ky, kz = kwant.continuum.momentum_operators
ham_rashba = kwant.continuum.sympify(
'''
B*g*mu_B/2*sigma_z+(hbar**2/(2*m_0)*(k_x/m*k_x+k_y/m*k_y+k_z/m*k_z)-V(x, y))*eye(2)+
alpha_z*(k_x*sigma_y-k_y*sigma_x)+alpha_y*(k_z*sigma_x-k_x*sigma_z)+alpha_x*(k_y*sigma_z-k_z*sigma_y)
''')
modified = ['V(x, y)']
ham_rashba = ham_rashba.subs(
{kx: kwant.continuum.sympify('k_x-pi/phi_0*B*y')})
ham1 = ham_rashba
ham2 = -ham_rashba.conjugate().subs({s: -s for s in [kx, ky, kz]})
hamiltonian = sympy.Matrix(sympy.BlockDiagMatrix(ham1, ham2))
hamiltonian[0, 3] = hamiltonian[3,
0] = +kwant.continuum.sympify('Delta_SC')
hamiltonian[1, 2] = hamiltonian[2,
1] = -kwant.continuum.sympify('Delta_SC')
subs = {s.conjugate(): s for s in hamiltonian.atoms(sympy.Symbol)}
subs.update({
kwant.continuum.sympify(m).conjugate(): kwant.continuum.sympify(m)
for m in modified
})
hamiltonian = hamiltonian.subs(subs)
template = discretize(hamiltonian, ('x', 'y'), grid_spacing=a)
wire = kwant.Builder()
shape = get_hexagon(width)
wire.fill(template, lambda s: shape([s.pos[0], s.pos[1]]), (0, 0))
return wire.finalized()
def block(self, ls, als, bs):
matrices = []
for i in range(len(als)):
matrixi = sp.Matrix([[als[i], -bs[i]], [bs[i], als[i]]])
matrices.append(matrixi)
B = sp.BlockDiagMatrix(sp.Matrix([ls]), *matrices)
return B
def get_foreman():
# Basis transformation
v_n = lambda i, N: sympy.Matrix( # noqa: E731
[1 if i == n else 0 for n in range(N)])
S, X, Y, Z = [v_n(i, 4) for i in range(4)]
up, dw = [v_n(i, 2) for i in range(2)]
X = sympy.I * X
Y = sympy.I * Y
Z = sympy.I * Z
molenkamp_basis = [
kr(up, S),
kr(dw, S),
+(1 / sympy.sqrt(2)) * kr(up, X + sympy.I * Y),
+(1 / sympy.sqrt(6)) * (kr(dw, X + sympy.I * Y) - kr(up, 2 * Z)),
-(1 / sympy.sqrt(6)) * (kr(up, X - sympy.I * Y) + kr(dw, 2 * Z)),
-(1 / sympy.sqrt(2)) * kr(dw, X - sympy.I * Y),
+(1 / sympy.sqrt(3)) * (kr(dw, X + sympy.I * Y) + kr(up, Z)),
+(1 / sympy.sqrt(3)) * (kr(up, X - sympy.I * Y) - kr(dw, Z)),
]
subs_notation = {
Ec: Ev + E0,
L: -(g1 + 4 * g2) * (hbar**2 / 2 / m0),
M: -(g1 - 2 * g2) * (hbar**2 / 2 / m0),
Np: -(3 * g3 + (3 * kappa + 1)) * (hbar**2 / 2 / m0),
Nm: -(3 * g3 - (3 * kappa + 1)) * (hbar**2 / 2 / m0),
Ac: (g0 * hbar**2 / 2 / m0),
}
Hs = spin_orbit()
Hcc = sympy.Matrix([Ec + kx * Ac * kx + ky * Ac * ky + kz * Ac * kz])
Hcv = +sympy.I * sympy.Matrix([[P * kx, P * ky, P * kz]])
Hvc = -sympy.I * sympy.Matrix([kx * P, ky * P, kz * P])
data = [[valence_term(i, j) for j in range(3)] for i in range(3)]
Hvv = sympy.Matrix(data)
H4 = sympy.BlockMatrix([[Hcc, Hcv], [Hvc, Hvv]])
H8 = sympy.Matrix(sympy.BlockDiagMatrix(H4, H4)) + Hs
dag = lambda x: x.conjugate().transpose() # noqa: E731
U_dag = sympy.Matrix(sympy.BlockMatrix([molenkamp_basis]))
U = dag(U_dag)
hamiltonian = U * H8 * dag(U)
hamiltonian = hamiltonian.subs(subs_notation)
hamiltonian = hamiltonian + (Ev - Delta / 3) * sympy.diag(
0, 0, 1, 1, 1, 1, 1, 1)
return sympy.ImmutableMatrix(hamiltonian.expand())
def _calc_covariance_matrix(self):
non_altered = []
means = []
blocks = []
names = []
for rvs, dist in self.distributions():
names.extend([rv.name for rv in rvs])
if isinstance(dist, stats.crv_types.NormalDistribution):
means.append(dist.mean)
blocks.append(sympy.Matrix([dist.std**2]))
elif isinstance(
dist, stats.joint_rv_types.MultivariateNormalDistribution):
means.extend(dist.mu)
blocks.append(dist.sigma)
else:
non_altered.extend(rvs)
if names:
M = sympy.BlockDiagMatrix(*blocks)
M = sympy.Matrix(M)
return means, M, names, non_altered
def _calc_covariance_matrix(self, ruv=False):
non_altered = []
means = []
blocks = []
names = []
if ruv:
dists = self.distributions(level=VariabilityLevel.RUV)
else:
dists = self.distributions(exclude_level=VariabilityLevel.RUV)
for rvs, dist in dists:
names.extend([rv.name for rv in rvs])
if isinstance(dist, stats.crv_types.NormalDistribution):
means.append(dist.mean)
blocks.append(sympy.Matrix([dist.std ** 2]))
elif isinstance(dist, stats.joint_rv_types.MultivariateNormalDistribution):
means.extend(dist.mu)
blocks.append(dist.sigma)
else:
non_altered.extend(rvs)
if names:
M = sympy.BlockDiagMatrix(*blocks)
M = sympy.Matrix(M)
return means, M, names, non_altered