phonon_lifetime package#

An Example project.

class phonon_lifetime.System#

Bases: ABC

Represents a System of atoms.

abstractmethod as_pristine() → PristineSystem#: Return a new System with no defects.

get_mode(idx: int) → NormalMode[__annotationlib_name_1__]#: Get the normal mode for a given index.

abstractmethod get_modes() → NormalModes[__annotationlib_name_1__]#: Get the normal modes of the system.

abstract property masses: ndarray[tuple[int], dtype[floating]]#: Mass of every atom in the system.

property n_atoms: int#: Number of atoms in the system.

abstract property n_primitive_atoms: int#: Number of atoms in the primitive cell.

abstract property n_repeats: tuple[int, int, int]#: Number of repeats of the primitive cell in each direction (nx, ny, nz).

abstract property primitive_atom_fractions: ndarray[tuple[int, int], dtype[floating]]#

The positions of the atoms as a fraction of the primitive cell.

primitive_atom_positions[i] is the position (x, y, z) of the i’th atom in the primitive cell.

abstract property primitive_cell: ndarray[tuple[int, int], dtype[floating]]#

Primitive cell lattice vectors.

primitive_cell[i] is the vector (x, y, z) for the i’th lattice vector of the primitive cell.

abstract property strain_tensor: ndarray[tuple[int, int, Literal[3], Literal[3]], dtype[float64]]#

Strain tensor matrix for the system.

strain_tensor[i, j, alpha, beta] is the force constant between the i’th and j’th atom in the system, for each pair of cartesian directions (alpha, beta).

abstract property symbols: list[str]#: Chemical symbol of every atom in the system.

Subpackages#

Submodules#

phonon_lifetime.forces module#

class phonon_lifetime.forces.PristineStrainTensor(*, data: ndarray[tuple[int, int, Literal[3], Literal[3]], dtype[float64]], n_repeats: tuple[int, int, int])#

Bases: object

Represents the strain tensor for a system of atoms.

calculate_full_tensor(n_repeats: tuple[int, int, int]) → ndarray[tuple[int, int, Literal[3], Literal[3]], dtype[float64]]#: Return the full strain tensor for a system with shape (n_repeats).

calculate_pristine_tensor(n_repeats: tuple[int, int, int]) → ndarray[tuple[int, int, Literal[3], Literal[3]], dtype[float64]]#: Return the pristine strain tensor for a system with shape (n_repeats).

data: ndarray[tuple[int, int, Literal[3], Literal[3]], dtype[float64]]#

property n_primitive_atoms: int#: Number of atoms in the primitive cell.

n_repeats: tuple[int, int, int]#

phonon_lifetime.forces.zero_strain_tensor(n_primitive_atoms: int) → PristineStrainTensor#: Return a zero strain tensor.

phonon_lifetime.lifetimes module#

phonon_lifetime.lifetimes.calculate_decay_rates(pristine: NormalModes, defects: NormalModes, *, time: float) → ndarray[tuple[int], dtype[float64]]#

Get the decay rate of each pristine state after a time t.

The transition rate according to first-order perturbation theory is given by Fermi’s Golden Rule: Gamma_i = sum_k |<p_k|V|p_i>|^2 / hbar^2 * [ 4 sin^2((omega_k - omega_i) * t / 2) / ((omega_k - omega_i) * t)^2 ] where |p_i> is the pristine state, |d_k> are the defect states. In the limit of t -> infinity, this reduces to the standard Fermi’s Golden Rule with a delta function enforcing energy conservation.

phonon_lifetime.lifetimes.calculate_finite_time_rates(pristine: NormalModes, defects: NormalModes, *, t: float) → ndarray[tuple[int], dtype[float64]]#: Calculate the finite-time decay rates of the pristine states after time t.

phonon_lifetime.lifetimes.calculate_survival_probabilities(pristine: NormalModes, defects: NormalModes, *, times: ndarray[tuple[int], dtype[float64]]) → ndarray[tuple[int], dtype[float64]]#

Get the survival probability of each pristine state after a time t.

returns an array of shape (n_pristine, n_times) where each element is the probability that the pristine state has not decayed after time t.

phonon_lifetime.lifetimes.calculate_survival_probability(pristine: NormalMode, defects: NormalModes, *, times: ndarray[tuple[int], dtype[float64]]) → ndarray[tuple[int], dtype[float64]]#

Get the survival probability of a pristine state after a time t.

returns an array of shape (n_times) where each element is the probability that the pristine state has not decayed after time t.

phonon_lifetime.lifetimes.get_first_order_scatter(pristine: NormalModes, defects: NormalModes) → ndarray[tuple[int, int], dtype[complex128]]#: Calculate the first-order scattering matrix element <p_k|V|p_i>.

phonon_lifetime.lifetimes.get_state_overlap(pristine: NormalMode, defects: NormalModes) → ndarray[tuple[int], dtype[complex128]]#: Calculate the overlap matrix S_ki = <d_k | p_i>.

phonon_lifetime.lifetimes.get_state_overlap_matrix(pristine: NormalModes, defects: NormalModes) → ndarray[tuple[int, int], dtype[complex128]]#: Calculate the overlap matrix S_ki = <d_k | p_i>.

phonon_lifetime.lifetimes.plot_first_order_scatter(pristine: NormalModes, defects: NormalModes, pristine_idx: int, *, ax: Axes | None = None) → tuple[Figure, Axes, Line2D]#

Plot the first-order scattering matrix element <p_k|V|p_i> against the defect frequencies.

for a pristine state |psi_i>, the first-order scattering with a defect mode k is given by $S_(omega_k)^i = |<bar{psi}_k|V|psi_i>|^2$ where omega_k is the frequency of the defect mode k.

phonon_lifetime.lifetimes.plot_first_order_scatter_against_qx(pristine: PristineModes, defects: NormalModes, pristine_idx: int, *, ax: Axes | None = None) → tuple[Figure, Axes, Line2D]#

Plot the first-order scattering matrix element <p_k|V|p_i> against the defect frequencies.

for a pristine state |psi_i>, the first-order scattering with a defect mode k is given by $S_(omega_k)^i = |<bar{psi}_k|V|psi_i>|^2$ where omega_k is the frequency of the defect mode k.

phonon_lifetime.lifetimes.plot_overlap_weights(pristine: NormalModes, defects: NormalModes, pristine_idx: int, *, ax: Axes | None = None) → tuple[Figure, Axes, Line2D]#

Plot the overlap weights of a pristine state with the defect states against the defect frequencies.

for a pristine state |psi_i>, the overlap weight with a defect mode k is given by $W_(omega_k)^i = |<bar{psi}_k|psi_i>|^2$ where omega_k is the frequency of the defect mode k.

phonon_lifetime.lifetimes.plot_survival_probability(pristine: NormalMode, defects: NormalModes, times: ndarray[tuple[int], dtype[float64]], *, ax: Axes | None = None) → tuple[Figure, Axes, Line2D]#: Plot the survival probabilities of the pristine states after time t.

phonon_lifetime.wannier module#

phonon_lifetime.wannier.plot_wannier_vector(modes: NormalModes, idx: int = 0, *, ax: Axes | None = None) → tuple[Figure, Axes]#: Plot the Wannier vectors of the system.