tkwant.onebody.kernels.PerturbationExtractor

class tkwant.onebody.kernels.PerturbationExtractor(syst, time_name, time_start, params=None)

Extract the time-dependent perturbation to the Hamiltonian.

The total Hamiltonian can be split into two parts: the stationary part and the time-dependent perturbation, i.e. H(t) = H_0 + W(t). This routine extracts the W(t) part from the Kwant system that specifies the H(t).

Parameters

  • syst (kwant.builder.FiniteSystem) – The system from which to extract the time-dependent perturbation.

  • time_name (str) – The name of the time argument. Only sites with Hamiltonian value functions with the argument name time_name are extracted into W(t).

  • time_start (float) – The initial time.

  • params (dict, optional) – Extra arguments to pass to the Hamiltonian of syst, excluding time.

Notes

By definition the perturbation is defined with respect to the initial time. The perturbation should be therefore zero for times t < time_start. This is not inforced by this routine however, but W(t) is always evaluated with the time argument it gets.

Methods

apply(self, double time, ket, out=None)

Evaluate the matrix-vector product W(t) @ ket for the given time.

Parameters

  • time (int or float) – Time argument, must be equal or larger than time_start.

  • out (numpy.ndarray, optional) – Sparse matrix with to perform the operation in-place. If provided, array must be zero on input.

Returns

out – The product W(t) @ ket. If an out argument is given, the operation is performed in-place and the routine returns None.

Return type

numpy.ndarray or None

data(self, double time, out=None)

Return the time-dependent matrix elements.

Parameters

  • time (int or float) – Time argument, must be equal or larger than time_start.

  • out (numpy.ndarray, optional) – Data array of the W(t) matrix for operation in-place.

Returns

out – Data array of the W(t) matrix (W(t).data). If an out argument is given, the operation is performed in-place and the routine returns None.

Return type

numpy.ndarray or None

empty(self)

Return an empty W(t) matrix with correct shape and indices.

Returns

out – An “empty” W(t) matrix filled with zeros.

Return type

coo_matrix

evaluate(self, double time, out=None)

Evaluate the W(t) matrix for the given time t.

Parameters

  • time (int or float) – Time argument, must be equal or larger than time_start.

  • out (coo_matrix, optional) – Sparse matrix with to perform the operation in-place.

Returns

out – The matrix W(t). The size of the W(t) matrix is size x size, containing nnz complex entries. If an out argument is given, the operation is performed in-place and the routine returns None.

Return type

coo_matrix or None

row_col(self)

Return the row and column vectors of the W(t) matrix.

Returns

  • row (np.ndarray) – Row vector of the W(t) matrix in coo format.

  • col (np.ndarray) – Column vector of the W(t) matrix in coo format.

Attributes

nnz

The total number of time-dependent matrix elements.

Returns

nnz – The total number of time-dependent matrix elements, equal to len(W(t).data).

Return type

int

size

The size of the W(t) matrix.

Returns

size – The size of the W(t) matrix is size x size.

Return type

int