def get_propagation(self, ham, psi_init, steps, dz, norm=False):
"""
Get the time evolution.
:param ham: sparse.csr_matrix. Tight-Binding Hamilonian.
:param psi_init: np.ndarray. Initial state.
:param steps: Positive Integer. Number of steps.
:param dz: Positive number. Step.
:param norm: Boolean. Default value True. Normalize the norm to 1 at each step.
"""
error_handling.empty_ham(ham)
error_handling.ndarray(psi_init, "psi_init", self.lat.sites)
error_handling.positive_int(steps, "steps")
error_handling.positive_real(dz, "dz")
error_handling.boolean(norm, "norm")
self.steps = steps
self.dz = dz
self.prop = np.empty((self.lat.sites, self.steps), "c16")
self.prop[:, 0] = psi_init
diag = 1j * np.ones(self.lat.sites, "c16")
A = (sparse.diags(diag, 0) - 0.5 * self.dz * ham).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * ham).toarray()
mat = np.dot(LA.inv(A), B)
for i in range(1, self.steps):
self.prop[:, i] = np.dot(mat, self.prop[:, i - 1])
if norm:
self.prop[:, i] /= np.abs(self.prop[:, i]).sum()
def get_propagation(self, ham, psi_init, steps, dz, norm=False):
'''
Get the time evolution.
:param ham: sparse.csr_matrix. Tight-Binding Hamilonian.
:param psi_init: np.ndarray. Initial state.
:param steps: Positive Integer. Number of steps.
:param dz: Positive number. Step.
:param norm: Boolean. Default value True. Normalize the norm to 1 at each step.
'''
error_handling.empty_ham(ham)
error_handling.ndarray(psi_init, 'psi_init', self.lat.sites)
error_handling.positive_int(steps, 'steps')
error_handling.positive_real(dz, 'dz')
error_handling.boolean(norm, 'norm')
self.steps = steps
self.dz = dz
self.prop = np.empty((self.lat.sites, self.steps), 'c16')
self.prop[:, 0] = psi_init
diag = 1j*np.ones(self.lat.sites, 'c16')
A = (sparse.diags(diag, 0) - 0.5 * self.dz * ham).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * ham).toarray()
mat = (np.dot(LA.inv(A), B))
for i in range(1, self.steps):
self.prop[:, i] = np.dot(mat, self.prop[:, i-1])
if norm:
self.prop[:, i] /= np.abs(self.prop[:, i]).sum()
def get_pumping(self, hams, psi_init, steps, dz, norm=True):
'''
Get the time evolution with adiabatic pumpings.
:param hams: List of sparse.csr_matrices. Tight-Binding Hamilonians.
:param psi_init: np.ndarray. Initial state.
:param steps: Positive integer. Number of steps.
:param dz: Positive number. Step.
:param norm: Boolean. Default value True. Normalize the norm to 1 at each step.
'''
error_handling.get_pump(hams)
error_handling.ndarray(psi_init, 'psi_init', self.lat.sites)
error_handling.positive_int(steps, 'steps')
error_handling.positive_real(dz, 'dz')
error_handling.boolean(norm, 'norm')
self.steps = steps
self.dz = dz
no = len(hams)
self.prop = np.empty((self.lat.sites, self.steps), 'c16')
self.prop[:, 0] = psi_init
diag = 1j * np.ones(self.lat.sites, 'c16')
delta = self.steps // (1 + no)
A = (sparse.diags(diag, 0) - 0.5 * self.dz * hams[0]).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * hams[0]).toarray()
mat = (np.dot(LA.inv(A), B))
# before pumping
for i in range(1, delta):
self.prop[:, i] = np.dot(mat, self.prop[:, i-1])
if norm:
self.prop[:, i] /= np.abs(self.prop[:, i]).sum()
# pumping
c = np.linspace(0, 1, delta)
for j in range(0, no-1):
for i in range(0, delta):
ham = (1-c[i])*hams[j]+c[i]*hams[j+1]
A = (sparse.diags(diag, 0) - 0.5 * self.dz * ham).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * ham).toarray()
mat = (np.dot(LA.inv(A), B))
self.prop[:, (j+1)*delta+i] = np.dot(mat, self.prop[:, (j+1)*delta+i-1])
if norm:
self.prop[:, (j+1)*delta+i] /= \
np.abs(self.prop[:, (j+1)*delta+i]).sum()
# after pumping
j = no
for i in range(0, self.steps - no*delta):
self.prop[:, no*delta+i] = np.dot(mat, self.prop[:, no*delta+i-1])
if norm:
self.prop[:, no*delta+i] /= np.abs(self.prop[:, no*delta+i]).sum()
def get_pumping(self, hams, psi_init, steps, dz, norm=True):
"""
Get the time evolution with adiabatic pumpings.
:param hams: List of sparse.csr_matrices. Tight-Binding Hamilonians.
:param psi_init: np.ndarray. Initial state.
:param steps: Positive integer. Number of steps.
:param dz: Positive number. Step.
:param norm: Boolean. Default value True. Normalize the norm to 1 at each step.
"""
error_handling.get_pump(hams)
error_handling.ndarray(psi_init, "psi_init", self.lat.sites)
error_handling.positive_int(steps, "steps")
error_handling.positive_real(dz, "dz")
error_handling.boolean(norm, "norm")
self.steps = steps
self.dz = dz
no = len(hams)
self.prop = np.empty((self.lat.sites, self.steps), "c16")
self.prop[:, 0] = psi_init
diag = 1j * np.ones(self.lat.sites, "c16")
delta = self.steps // (1 + no)
A = (sparse.diags(diag, 0) - 0.5 * self.dz * hams[0]).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * hams[0]).toarray()
mat = np.dot(LA.inv(A), B)
# before pumping
for i in range(1, delta):
self.prop[:, i] = np.dot(mat, self.prop[:, i - 1])
if norm:
self.prop[:, i] /= np.abs(self.prop[:, i]).sum()
# pumping
c = np.linspace(0, 1, delta)
for j in range(0, no - 1):
for i in range(0, delta):
ham = (1 - c[i]) * hams[j] + c[i] * hams[j + 1]
A = (sparse.diags(diag, 0) - 0.5 * self.dz * ham).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * ham).toarray()
mat = np.dot(LA.inv(A), B)
self.prop[:, (j + 1) * delta + i] = np.dot(mat, self.prop[:, (j + 1) * delta + i - 1])
if norm:
self.prop[:, (j + 1) * delta + i] /= np.abs(self.prop[:, (j + 1) * delta + i]).sum()
# after pumping
j = no
for i in range(0, self.steps - no * delta):
self.prop[:, no * delta + i] = np.dot(mat, self.prop[:, no * delta + i - 1])
if norm:
self.prop[:, no * delta + i] /= np.abs(self.prop[:, no * delta + i]).sum()
def ani(self, ani, name, fps=10):
error_handling.ani(ani)
error_handling.string(name, 'name')
error_handling.positive_int(fps, 'fps')
name_file = self.dir_name + '/' + name + '.mp4'
ani.save(name_file, fps=fps, extra_args=['-vcodec', 'libx264'])
def ani(self, ani, name, fps=10):
error_handling.ani(ani)
error_handling.string(name, 'name')
error_handling.positive_int(fps, 'fps')
name_file = self.dir_name + '/' + name + '.mp4'
ani.save(name_file, fps=fps, extra_args=['-vcodec', 'libx264'])