This module contains core computational routines. More...

Functions/Subroutines
subroutine	evaluate_error (Delta_CVec, Delta_Psi, rho_jk_zero, CVecError, PsiError, nConf)
	This routine estimates the error of a propagation/relaxation step. The error estimator is documented in [M.H. Beck, H.D. Meyer, Z. f. Phys. D 42 113 (1997)].
subroutine	FuncOrbs (AbsTime, Psi_WORK, DtPsi_WORK, CData, RData, IData, LData)
	This routine returns the RHS of the orbital equation of motion. The routine FuncOrbs is given to the ABM integrator of the abmlib of MCTDH.
subroutine	FuncCVecBandMat (AbsTime, CVec, DtCVec, BandMat, RData, IData, LData)
	This routine returns the RHS of the coefficent equation of motion. The routine FuncCVec is given to the SIL integrator of the sillib of MCTDH returns -i H\|CVec> or -H\|CVec> as DtCVec using the Band Matrix routine to comply with the SILstep routine StdForm flag.
subroutine	get_FullHamiltonianBandMatrix (NPar, MOrb, NDX, NDY, NDZ, Dims, nConf, nSuperDiags, lambda0, Psi, BandMat)
	This routine returns the Hamiltonian matrix <n\|H\|n'> for M=1,2 orbitals. The matrix is then a simple band matrix and can be given to the LAPACK routine ZHBMV.
subroutine	projector_MCTDHB (Chi, projectedChi, Psi)
	This routine implements the MCTDHB projector P given a vector of MOrb orbitals Psi_j = Psi(:,k), j=k,...,M, the SUBROUTINE returns the projection.
subroutine	get_hPsi (MOrb, NDX, NDY, NDZ, Dims, Psi, hPsi)
	This routine computes the vectors h\|psi_1>, ..., h\|psi_MOrb>, where the psi_j j=1,...,MOrb are the orbitals used. This function uses Fourier transform of the ACML library to compute the kinetic part of the one-body Hamiltonian. (the mass m and hbar are set to one, everywhere)
subroutine	get_Wsl_IMEST (Wsl, psi_s, psi_l)
	This routine evaluates Wsl using the IMEST algorithm. It needs vtilde as an input, either from get_vtilde or calculated analytically. vtilde is nothing but the Fourier transform of the interaction potential times (2pi)^(D/2) / dV where dV is the volume element of a grid point in D dimensions. The vector is orderd in FFT order.
subroutine	get_vtilde (NDX, NDY, NDZ, Dims, xi, xf, yi, yf, zi, zf, vtilde)
	This routine computes vtilde for the IMEST algorithm. It calls Wint_IMEST as interaction potential. vtilde is nothing but the Fourier transform W(k) of the interaction potential times (2pi)^(D/2) / dV. The vector is stored in FFT order. The following definition of the Fourier transform is used.
subroutine	get_h_jk (Psi, h_jk, NDX, NDY, NDZ, Dims, MOrb)
	This routine returns the matrix elements h_jk = <Psi_j\|h\|Psi_k> of the one-body part of the many-body Hamiltonian.
subroutine	get_Wsl (Wsl, s, l, Psi)
	This routine computes the vector Wsl(x) = Int[psi_s^*(x') W(x-x') psi_l(x')].
subroutine	get_Wsl_phi_q (Wsl, phi_q, Wsl_phi_q)
	This routine multiplies Wsl(x) with psi_q.
subroutine	get_Wijkl (Wijkl, i, j, k, l, Psi)
	This routine computes the interaction matrix element W_ijkl.
subroutine	get_rho_jk (nConf, MOrb, NPar, CVec, rho_jk)
	This routine computes the matrix elements of the reduced one-body density matrix rho_jk for MOrb=1,2 orbitals.
subroutine	get_rho_ijkl (nConf, MOrb, NPar, CVec, rho_ijkl)
	This routine computes the matrix elements of the reduced two-body density matrix rho_ijkl for MOrb=1,2 orbitals.
subroutine	get_mu_kj (AbsTime, mu_kj, Psi, rho_jk, rho_ijkl)
	This routine returns the chemical potentials mu_kj.

Detailed Description

This module contains core computational routines.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: variable documentation

Function/Subroutine Documentation

subroutine modulecomputationcore::evaluate_error	(	COMPLEX*16,dimension(nconf),intent(in)	Delta_CVec,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Delta_Psi,
		COMPLEX*16,dimension(morb,morb),intent(in)	rho_jk_zero,
		REAL*8,intent(inout)	CVecError,
		REAL*8,intent(inout)	PsiError,
		INTEGER*4,intent(in)	nConf
	)

This routine estimates the error of a propagation/relaxation step. The error estimator is documented in [M.H. Beck, H.D. Meyer, Z. f. Phys. D 42 113 (1997)].

Authors:: Kaspar Sakmann (2008)

Since:: 2008

Todo:: make MOrb an inputvariable and get rid of the use association

Definition at line 21 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::FuncCVecBandMat	(	REAL*8,intent(in)	AbsTime,
		COMPLEX*16,dimension(nconf),intent(in)	CVec,
		COMPLEX*16,dimension(nconf),intent(out)	DtCVec,
		COMPLEX*16,dimension(nsuperdiags+1,nconf),intent(in)	BandMat,
		REAL*8,dimension(10),intent(in)	RData,
		INTEGER,dimension(30),intent(in)	IData,
		logical,intent(in)	LData
	)

This routine returns the RHS of the coefficent equation of motion. The routine FuncCVec is given to the SIL integrator of the sillib of MCTDH returns -i H|CVec> or -H|CVec> as DtCVec using the Band Matrix routine to comply with the SILstep routine StdForm flag.

Authors:: Kaspar Sakmann (2008)

Since:: 2008

Todo:: put all use associated variables into IDATA,RDATA CDATA and LDATA

Definition at line 235 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::FuncOrbs	(	REAL*8,intent(in)	AbsTime,
		COMPLEX16,dimension(ndxndyndzmorb),intent(inout)	Psi_WORK,
		COMPLEX16,dimension(ndxndyndzmorb),intent(out)	DtPsi_WORK,
		COMPLEX*16,dimension(morb,morb,morb,morb,2),intent(in)	CData,
		REAL*8,dimension(10)	RData,
		INTEGER,dimension(30),intent(in)	IData,
		logical,intent(in)	LData
	)

This routine returns the RHS of the orbital equation of motion. The routine FuncOrbs is given to the ABM integrator of the abmlib of MCTDH.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: put all use associated variables into IDATA,RDATA CDATA and LDATA

Definition at line 73 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_FullHamiltonianBandMatrix	(	INTEGER,intent(in)	NPar,
		INTEGER,intent(in)	MOrb,
		INTEGER,intent(in)	NDX,
		INTEGER,intent(in)	NDY,
		INTEGER,intent(in)	NDZ,
		INTEGER,intent(in)	Dims,
		INTEGER,intent(in)	nConf,
		INTEGER,intent(in)	nSuperDiags,
		REAL*8,intent(in)	lambda0,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi,
		COMPLEX*16,dimension(nsuperdiags+1,nconf),intent(out)	BandMat
	)

This routine returns the Hamiltonian matrix <n|H|n'> for M=1,2 orbitals. The matrix is then a simple band matrix and can be given to the LAPACK routine ZHBMV.

Authors:: Kaspar Sakmann (2008)

Since:: 2008

Todo:: for more than 2 orbitals this is not a good idea because the matrix will no longer be a simple band matrix. Use, e.g. the mapping fo rmore orbitals.

Definition at line 283 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_h_jk	(	COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi,
		COMPLEX*16,dimension(morb,morb),intent(out)	h_jk,
		INTEGER,intent(in)	NDX,
		INTEGER,intent(in)	NDY,
		INTEGER,intent(in)	NDZ,
		INTEGER,intent(in)	Dims,
		INTEGER,intent(in)	MOrb
	)

This routine returns the matrix elements h_jk = <Psi_j|h|Psi_k> of the one-body part of the many-body Hamiltonian.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Definition at line 810 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_hPsi	(	intEGER,intent(in)	MOrb,
		intEGER,intent(in)	NDX,
		intEGER,intent(in)	NDY,
		intEGER,intent(in)	NDZ,
		intEGER,intent(in)	Dims,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(out)	hPsi
	)

This routine computes the vectors h|psi_1>, ..., h|psi_MOrb>, where the psi_j j=1,...,MOrb are the orbitals used. This function uses Fourier transform of the ACML library to compute the kinetic part of the one-body Hamiltonian. (the mass m and hbar are set to one, everywhere)

h(x) = p^2/2m + V_ext(x) if Dims=1

h(x,y) = p^2/2m + V_ext(x,y) if Dims=2

h(x,y,z) = p^2/2m + V_ext(x,y,z) if Dims=3

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Definition at line 442 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_mu_kj	(	REAL*8,intent(in)	AbsTime,
		COMPLEX*16,dimension(morb,morb),intent(out)	mu_kj,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi,
		COMPLEX*16,dimension(morb,morb),intent(in)	rho_jk,
		COMPLEX*16,dimension(morb,morb,morb,morb),intent(in)	rho_ijkl
	)

This routine returns the chemical potentials mu_kj.

Authors:: Kaspar Sakmann (2012)

Since:: 2012

Definition at line 1078 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_rho_ijkl	(	INTEGER,intent(in)	nConf,
		INTEGER,intent(in)	MOrb,
		INTEGER,intent(in)	NPar,
		COMPLEX*16,dimension(nconf),intent(in)	CVec,
		COMPLEX*16,dimension(morb,morb,morb,morb),intent(out)	rho_ijkl
	)

This routine computes the matrix elements of the reduced two-body density matrix rho_ijkl for MOrb=1,2 orbitals.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: write it for MOrb=arbitrary orbitals

Definition at line 1000 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_rho_jk	(	INTEGER,intent(in)	nConf,
		INTEGER,intent(in)	MOrb,
		INTEGER,intent(in)	NPar,
		COMPLEX*16,dimension(nconf),intent(in)	CVec,
		COMPLEX*16,dimension(morb,morb),intent(out)	rho_jk
	)

This routine computes the matrix elements of the reduced one-body density matrix rho_jk for MOrb=1,2 orbitals.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: write it for MOrb=arbitrary orbitals

Definition at line 946 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_vtilde	(	INTEGER,intent(in)	NDX,
		INTEGER,intent(in)	NDY,
		INTEGER,intent(in)	NDZ,
		INTEGER,intent(in)	Dims,
		REAL*8,intent(in)	xi,
		REAL*8,intent(in)	xf,
		REAL*8,intent(in)	yi,
		REAL*8,intent(in)	yf,
		REAL*8,intent(in)	zi,
		REAL*8,intent(in)	zf,
		COMPLEX16,dimension(ndxndy*ndz),intent(out)	vtilde
	)

This routine computes vtilde for the IMEST algorithm. It calls Wint_IMEST as interaction potential. vtilde is nothing but the Fourier transform W(k) of the interaction potential times (2pi)^(D/2) / dV. The vector is stored in FFT order. The following definition of the Fourier transform is used.

W(k) = 1/(2pi)^(D/2) Int [dy W(y) exp(-iky)]

Here, y is the vector y=r_2-r_1 where r_1, r_2 are the position vectors of two particles.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Definition at line 693 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_Wijkl	(	COMPLEX*16,intent(out)	Wijkl,
		INTEGER,intent(in)	i,
		INTEGER,intent(in)	j,
		INTEGER,intent(in)	k,
		INTEGER,intent(in)	l,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi
	)

This routine computes the interaction matrix element W_ijkl.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: get rid of use associations, all variables as arguments.

Definition at line 913 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_Wsl	(	COMPLEX16,dimension(ndxndy*ndz),intent(out)	Wsl,
		INTEGER,intent(in)	s,
		INTEGER,intent(in)	l,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi
	)

This routine computes the vector Wsl(x) = Int[psi_s^*(x') W(x-x') psi_l(x')].

The default is a delta function interaction W(x-x') = lambda0 delta(x-x') if useIMEST = .FALSE. . In this case the result is Wsl(x) = lambda0 psi_s^*(x) psi_l(x)

If useIMEST = .TRUE. the potential defined in Wint_IMEST is used to compute Wsl. The IMEST algorithm requires that the value of the interaction potential W(r_1,r_2) depends only on the position difference between two particles r_2-r_1, e.g. for a gaussian or 1/r^3 interaction.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: get rid of use associations, all variables as arguments. reduce module dependencies. currently

Definition at line 853 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_Wsl_IMEST	(	COMPLEX16,dimension(ndxndy*ndz),intent(out)	Wsl,
		COMPLEX16,dimension(ndxndy*ndz),intent(in)	psi_s,
		COMPLEX16,dimension(ndxndy*ndz),intent(in)	psi_l
	)

This routine evaluates Wsl using the IMEST algorithm. It needs vtilde as an input, either from get_vtilde or calculated analytically. vtilde is nothing but the Fourier transform of the interaction potential times (2pi)^(D/2) / dV where dV is the volume element of a grid point in D dimensions. The vector is orderd in FFT order.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: documentation still missing

the get_Wsl function needs to be streamlined to be able to switch between delta interaction and IMEST, vtilde should stay use associated to minimize the computational effort.

for time-dependent interaction strengths needs to be multiplied by the appropriate factor in the main program. do not recompute vtilde!

it would be nice to provide an option where vtilde is read in from an analytic calculation, e.g. for dipolar interaction or exponentially decaying ineraction

Definition at line 573 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::get_Wsl_phi_q	(	COMPLEX16,dimension(ndxndy*ndz),intent(in)	Wsl,
		COMPLEX16,dimension(ndxndy*ndz),intent(in)	phi_q,
		COMPLEX16,dimension(ndxndy*ndz),intent(out)	Wsl_phi_q
	)

This routine multiplies Wsl(x) with psi_q.

Authors:: Kaspar Sakmann (2007)

Since:: 2007

Todo:: get rid of use associations, all variables as arguments.

Definition at line 889 of file modulecomputationcore.F90.

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subroutine modulecomputationcore::projector_MCTDHB	(	COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Chi,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(out)	projectedChi,
		COMPLEX16,dimension(ndxndy*ndz,morb),intent(in)	Psi
	)

This routine implements the MCTDHB projector P given a vector of MOrb orbitals Psi_j = Psi(:,k), j=k,...,M, the SUBROUTINE returns the projection.

projected_Chi(:,j) = [1 - Sum_{k=1}^MOrb |Psi_k><Psi_k|] Chi(:,k) = P Chi(:,k)

Authors:: Kaspar Sakmann (2008)

Since:: 2008

Todo:: get rid of the use association

Definition at line 378 of file modulecomputationcore.F90.

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modulecomputationcore Module Reference

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation