A module to add in common quantum dynamical operations. More...

Functions/Subroutines
subroutine, public	prg_kick_density (kick_direc, kick_mag, dens, norbs, mdim, S, SINV, which_atom, r, bmltype, thresh)
	Provides perturbation to initial density matrix in the form of an electric field kick. This routine does: \(\hat{\rho_{kick}} = \exp{\frac{-i}{\hbar}\hat{V}}\hat{\rho}\hat{S}\exp{\frac{i}{\hbar}\hat{V}}\hat{S^{-1}}\) where \(\hat{V}\) is the field disturbance. More...

subroutine, public	prg_get_sparsity_cplxmat (matrix_type, element_type, thresh, a_dense)
	This computes the sparsity of a complex matrix given a threshold value This routine does: \( f = \frac{N_0}{N_{tot}}\) where \(f\) is the sparsity, \(N_0\) is the number of values less than the threshold, and \(N_{tot}\) is the total number of values. The sparsity and threshold are printed to the screen. More...

subroutine, public	prg_get_sparsity_realmat (matrix_type, element_type, thresh, a_dense)
	This computes the sparsity of a real matrix given a threshold value This routine does: \( f = \frac{N_0}{N_{tot}}\) where \(f\) is the sparsity, \(N_0\) is the number of values less than the threshold, and \(N_{tot}\) is the total number of values. The sparsity and threshold are printed to the screen. More...

subroutine, public	prg_kick_density_bml (kick_direc, kick_mag, rho_bml, s_bml, sinv_bml, mdim, which_atom, r, matrix_type, thresh)
	Provides perturbation to initial density matrix in the form of an electric field kick given input matricies in BML format. This routine does: \(\hat{\rho_{kick}} = \exp{\frac{-i}{\hbar}\hat{V}}\hat{\rho}\hat{S}\exp{\frac{i}{\hbar}\hat{V}}\hat{S^{-1}}\) where \(\hat{V}\) is the field disturbance. More...

subroutine, public	prg_lvni_bml (h1_bml, sinv_bml, dt, hbar, rhoold_bml, rho_bml, aux_bml, matrix_type, mdim, thresh)
	Performs Liouville-von Neumann integration using leap-frog method. This routine does: \(\hat{\rho}(t+\Delta t)=\hat{\rho}(t-\Delta t) +2\Delta t\frac{\partial \hat{\rho}(t)}{\partial t}\) where the time derivative of the density matrix is defined as follows: \(\frac{\partial\hat{\rho}(t)}{\partial t}=\frac{-i}{\hbar}\left(S^{-1}\hat{H}(t)\hat{\rho}(t)-\hat{\rho}(t)\hat{H}(t)S^{-1}\right)\). More...

subroutine, public	prg_getcharge (rho_bml, s_bml, charges, aux_bml, z, spindex, N, nats, thresh)
	Constructs the charges from the density matrix. More...

subroutine, public	prg_getdipole (charges, r, mu)
	This routine computes the dipole moment of the system with units determined by the units of the coordinate matrix and charges given. More...

subroutine, public	prg_excitation (fill_mat, orbit_orig, orbit_exci)
	Produce an excitation in the initially calculated density matrix to. More...

Variables
integer, parameter	dp = kind(1.0d0)

Detailed Description

A module to add in common quantum dynamical operations.

This module contains routines that perform the following tasks: apply a apply an excitation or perturbation to the initial density matrix, compute the comutator of two two matricies, calculate the sparsity of a real or complex matrix, and time evolve a density matrix using Liouville-von Neumann equation with the leap-frog method of integration.

Function/Subroutine Documentation

◆ prg_excitation()

subroutine, public prg_quantumdynamics_mod::prg_excitation	(	integer, dimension(:), intent(inout)	fill_mat,
		integer, intent(in)	orbit_orig,
		integer, intent(in)	orbit_exci
	)

Produce an excitation in the initially calculated density matrix to.

Definition at line 306 of file prg_quantumdynamics_mod.F90.

◆ prg_get_sparsity_cplxmat()

subroutine, public prg_quantumdynamics_mod::prg_get_sparsity_cplxmat	(	character(len=*), intent(in)	matrix_type,
		character(len=*), intent(in)	element_type,
		real(dp), intent(in)	thresh,
		complex(dp), dimension(:,:), intent(in)	a_dense
	)

This computes the sparsity of a complex matrix given a threshold value This routine does: \( f = \frac{N_0}{N_{tot}}\) where \(f\) is the sparsity, \(N_0\) is the number of values less than the threshold, and \(N_{tot}\) is the total number of values. The sparsity and threshold are printed to the screen.

Parameters

matrix_type	the BML matrix type
element_type	the BML element type
thresh	the threshold for sparsity evaluation
a_dense	the dense complex matrix to be evaluated for sparsity

Definition at line 97 of file prg_quantumdynamics_mod.F90.

◆ prg_get_sparsity_realmat()

subroutine, public prg_quantumdynamics_mod::prg_get_sparsity_realmat	(	character(len=*), intent(in)	matrix_type,
		character(len=*), intent(in)	element_type,
		real(dp), intent(in)	thresh,
		real(dp), dimension(:,:), intent(in)	a_dense
	)

This computes the sparsity of a real matrix given a threshold value This routine does: \( f = \frac{N_0}{N_{tot}}\) where \(f\) is the sparsity, \(N_0\) is the number of values less than the threshold, and \(N_{tot}\) is the total number of values. The sparsity and threshold are printed to the screen.

Parameters

matrix_type	the BML matrix type
element_type	the BML element type
thresh	the threshold for sparsity evaluation
a_dense	the dense real matrix to be evaluated for sparsity

Definition at line 121 of file prg_quantumdynamics_mod.F90.

◆ prg_getcharge()

subroutine, public prg_quantumdynamics_mod::prg_getcharge	(	type(bml_matrix_t), intent(in)	rho_bml,
		type(bml_matrix_t), intent(in)	s_bml,
		real(dp), dimension(:), allocatable	charges,
		type(bml_matrix_t)	aux_bml,
		real(dp), dimension(:), intent(in)	z,
		integer, dimension(:), intent(in), allocatable	spindex,
		integer, dimension(:), intent(in), allocatable	N,
		integer	nats,
		real(dp), intent(in)	thresh
	)

Constructs the charges from the density matrix.

Parameters

rho_bml	Density matrix in BML format.
over_bml	Overlap matrix in BML format.
charges	the array of charges.
aux_bml	the auxiliary matrix in BML format.
spindex	Start and end index for every atom in the system.
z
nats	the number of atoms
N
thresh	threshold for the BML matrix

Definition at line 246 of file prg_quantumdynamics_mod.F90.

◆ prg_getdipole()

subroutine, public prg_quantumdynamics_mod::prg_getdipole	(	real(dp), dimension(:), intent(in)	charges,
		real(dp), dimension(:,:), intent(in)	r,
		real(dp), dimension(3), intent(inout)	mu
	)

This routine computes the dipole moment of the system with units determined by the units of the coordinate matrix and charges given.

Parameters

charges	Charge on each atom.
r	Coordinate matrix of the atoms.
p	Dipole moment vector.

Definition at line 281 of file prg_quantumdynamics_mod.F90.

◆ prg_kick_density()

subroutine, public prg_quantumdynamics_mod::prg_kick_density	(	integer, intent(in)	kick_direc,
		real(dp)	kick_mag,
		complex(dp), dimension(:,:), intent(inout), allocatable	dens,
		integer, intent(in)	norbs,
		integer, intent(in)	mdim,
		complex(dp), dimension(:,:), allocatable	S,
		complex(dp), dimension(:,:), allocatable	SINV,
		integer, dimension(:), intent(in), allocatable	which_atom,
		real(dp), dimension(:,:), allocatable	r,
		character(len=*), intent(in)	bmltype,
		real(dp)	thresh
	)

Provides perturbation to initial density matrix in the form of an electric field kick. This routine does: \(\hat{\rho_{kick}} = \exp{\frac{-i}{\hbar}\hat{V}}\hat{\rho}\hat{S}\exp{\frac{i}{\hbar}\hat{V}}\hat{S^{-1}}\) where \(\hat{V}\) is the field disturbance.

Parameters

kick_direc	the direction of the kick in the electric field
kick_mag	the magnitude of the kick in the electric field
dens	the initial density matrix to be kicked.
norbs	the number of orbitals in the density matrix
S	the overlap matrix
SINV	the inverse of the overlap matrix
which_atom	vector containing atom identification
r	direction vector for kick based on atom and kick_direc
bmltype	type of BML matrix desired for faster computation
thresh	threshold for BML matrix conversion

Definition at line 41 of file prg_quantumdynamics_mod.F90.

◆ prg_kick_density_bml()

subroutine, public prg_quantumdynamics_mod::prg_kick_density_bml	(	integer, intent(in)	kick_direc,
		real(dp)	kick_mag,
		type(bml_matrix_t)	rho_bml,
		type(bml_matrix_t)	s_bml,
		type(bml_matrix_t)	sinv_bml,
		integer	mdim,
		integer, dimension(:), intent(in), allocatable	which_atom,
		real(dp), dimension(:,:), allocatable	r,
		character(len=*), intent(in)	matrix_type,
		real(dp)	thresh
	)

Provides perturbation to initial density matrix in the form of an electric field kick given input matricies in BML format. This routine does: \(\hat{\rho_{kick}} = \exp{\frac{-i}{\hbar}\hat{V}}\hat{\rho}\hat{S}\exp{\frac{i}{\hbar}\hat{V}}\hat{S^{-1}}\) where \(\hat{V}\) is the field disturbance.

Parameters

kick_direc	the direction of the kick in the electric field
kick_mag	the magnitude of the kick in the electric field
rho_bml	the initial density matrix to be kicked in BML format.
s_bml	the overlap matrix
sinv_bml	the inverse of the overlap matrix
mdim	maximum number of nonzero values per row in BML matrix
which_atom	vector containing atom identification
r	position vector for kicked atom
matrix_type	the type of BML format
thresh	the threshold for the BML matrix

Definition at line 152 of file prg_quantumdynamics_mod.F90.

◆ prg_lvni_bml()

subroutine, public prg_quantumdynamics_mod::prg_lvni_bml	(	type(bml_matrix_t)	h1_bml,
		type(bml_matrix_t)	sinv_bml,
		real(dp)	dt,
		real(dp)	hbar,
		type(bml_matrix_t)	rhoold_bml,
		type(bml_matrix_t)	rho_bml,
		type(bml_matrix_t)	aux_bml,
		character(len=*), intent(in)	matrix_type,
		integer	mdim,
		real(dp), intent(in)	thresh
	)

Performs Liouville-von Neumann integration using leap-frog method. This routine does: \(\hat{\rho}(t+\Delta t)=\hat{\rho}(t-\Delta t) +2\Delta t\frac{\partial \hat{\rho}(t)}{\partial t}\) where the time derivative of the density matrix is defined as follows: \(\frac{\partial\hat{\rho}(t)}{\partial t}=\frac{-i}{\hbar}\left(S^{-1}\hat{H}(t)\hat{\rho}(t)-\hat{\rho}(t)\hat{H}(t)S^{-1}\right)\).

Parameters

H	the Hamiltonian matrix at time t
sinv_bml	the inverse overlap matrix
dt	the timestep for integration
hbar	the Dirac constant (generally taken to be 1 in simulation units)
rho_old	the density matrix at previous time-step
rho_bml	the density matrix at current time-step
aux_bml	the temp matrix used for value storage during computation
matrix_type	the type of BML matrix
thresh	the threshold for the BML matrix