Example #1
0
    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()
Example #2
0
    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()
Example #3
0
    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()
Example #4
0
    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()
Example #5
0
File: save.py Project: cpoli/tbee
 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'])
Example #6
0
 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'])