Source code for iDEA.methods.hartree

"""Contains all Hartree functionality and solvers."""


from collections.abc import Callable
import numpy as np
import iDEA.system
import iDEA.state
import iDEA.observables
import iDEA.methods.non_interacting


name = "hartree"


kinetic_energy_operator = iDEA.methods.non_interacting.kinetic_energy_operator
external_potential_operator = iDEA.methods.non_interacting.external_potential_operator


[docs]def hartree_potential_operator(s: iDEA.system.System, n: np.ndarray) -> np.ndarray: r""" Compute the Hartree potential operator. | Args: | s: iDEA.system.System, System object. | n: np.ndarray, Charge density. | Returns: | Vh: np.ndarray, Hartree potential energy operator. """ v_h = iDEA.observables.hartree_potential(s, n) Vh = np.diag(v_h) return Vh
[docs]def hamiltonian( s: iDEA.system.System, up_n: np.ndarray, down_n: np.ndarray, up_p: np.ndarray, down_p: np.ndarray, K: np.ndarray = None, Vext: np.ndarray = None, ) -> np.ndarray: r""" Compute the Hamiltonian from the kinetic and potential terms. | Args: | s: iDEA.system.System, System object. | up_n: np.ndarray, Charge density of up electrons. | down_n: np.ndarray, Charge density of down electrons. | up_p: np.ndarray, Charge density matrix of up electrons. | down_p: np.ndarray, Charge density matrix of down electrons. | K: np.ndarray, Single-particle kinetic energy operator [If None this will be computed from s]. (default = None) | Vext: np.ndarray, Potential energy operator [If None this will be computed from s]. (default = None) | Returns: | H: np.ndarray, Hamiltonian, up Hamiltonian, down Hamiltonian. """ if K is None: K = kinetic_energy_operator(s) if Vext is None: Vext = external_potential_operator(s) Vh = hartree_potential_operator(s, up_n + down_n) H = K + Vext + Vh return H, H, H
[docs]def total_energy(s: iDEA.system.System, state: iDEA.state.SingleBodyState) -> float: r""" Compute the total energy. | Args: | s: iDEA.system.System, System object. | state: iDEA.state.SingleBodyState, State. (default = None) | Returns: | E: float, Total energy. """ E = iDEA.observables.single_particle_energy(s, state) n = iDEA.observables.density(s, state) v_h = iDEA.observables.hartree_potential(s, n) E -= 0.5 * iDEA.observables.hartree_energy(s, n, v_h) return E
[docs]def solve( s: iDEA.system.System, k: int = 0, restricted: bool = False, mixing: float = 0.5, tol: float = 1e-10, initial: tuple = None, silent: bool = False, ) -> iDEA.state.SingleBodyState: r""" Solves the Schrodinger equation for the given system. | Args: | s: iDEA.system.System, System object. | k: int, Energy state to solve for. (default = 0, the ground-state) | restricted: bool, Is the calculation restricted (r) on unrestricted (u). (default=False) | mixing: float, Mixing parameter. (default = 0.5) | tol: float, Tollerance of convergence. (default = 1e-10) | initial: tuple. Tuple of initial values used to begin the self-consistency (n, up_n, down_n, p, up_p, down_p). (default = None) | silent: bool, Set to true to prevent printing. (default = False) | Returns: | state: iDEA.state.SingleBodyState, Solved state. """ return iDEA.methods.non_interacting.solve( s, hamiltonian, k, restricted, mixing, tol, initial, name, silent )
[docs]def propagate( s: iDEA.system.System, state: iDEA.state.SingleBodyState, v_ptrb: np.ndarray, t: np.ndarray, hamiltonian_function: Callable = None, restricted: bool = False, ) -> iDEA.state.SingleBodyEvolution: r""" Propagate a set of orbitals forward in time due to a dynamic local pertubation. | Args: | s: iDEA.system.System, System object. | state: iDEA.state.SingleBodyState, State to be propigated. | v_ptrb: np.ndarray, Local perturbing potential on the grid of t and x values, indexed as v_ptrb[time,space]. | t: np.ndarray, Grid of time values. | hamiltonian_function: Callable, Hamiltonian function [If None this will be the non_interacting function]. (default = None) | restricted: bool, Is the calculation restricted (r) on unrestricted (u). (default=False) | Returns: | evolution: iDEA.state.SingleBodyEvolution, Solved time-dependent evolution. """ return iDEA.methods.non_interacting.propagate( s, state, v_ptrb, t, hamiltonian, restricted, name )