Most applications of time-dependent density-functional theory (TDDFT)
use the adiabatic local-density approximation (ALDA) for the dynamical
exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic)
extension of the ground-state LDA into the dynamical regime leads
to a Vxc(r,t) with a memory, which causes the electron dynamics to
become dissipative. To illustrate and explain this nonadiabatic behavior,
this paper studies the dynamics of two interacting electrons on a
two-dimensional quantum strip of finite size, comparing TDDFT within
and beyond the ALDA with numerical solutions of the two-electron
time-dependent Schrödinger equation. It is shown explicitly how dissipation
arises through multiple particle-hole excitations, and how the nonadiabatic
extension of the ALDA fails for finite systems but becomes correct
in the thermodynamic limit.
Description
Time dependent density functional theory; Memory effects kernel; breakdown adiabatic approximation
Nice Intro/Review on relaxation/dissipation effects
2 el in a 2D quantum strip of finite length L
Exact Solution vs ALDA and ALDA+M (memory) TD evolution
The dipole moment in ALDA and exact solution oscillates at the frequency,
only in the exact a beat is visible due to the coupling between single
and double excitations.
Within TD-KS this effect has to be reproduced by the non-adiabacity
of the xc potential. The non adiabatic part of the potential will
act as a dissipative force.
ALDA+M may be fine as non adiabatic approximation for infinite system,
but for finite systems produce artificial dissipative effects due
to the unphysical coupling to continua of multi particle-hole excitations
that are implicitly contained in hom el liquid
For a non finite systems: extrapolation for L->ınfty: the beat oscillation
wavelenght is proportional to L, if L goes to infinity the beat oscillation
becomes a "dissipation"
NB Energy is always conserved, so (at least in finite system) there
is a trasfer of energy between two sets of electronic degrees of
freedom coupled trough Coulombic
%0 Journal Article
%1 Ullrich2006a
%A Ullrich, C. A.
%D 2006
%I AIP
%J The Journal of Chemical Physics
%K Schrodinger correlations density electron equation; functional ground states; theory;
%N 23
%P 234108
%R 10.1063/1.2406069
%T Time-dependent density-functional theory beyond the adiabatic approximation:
Insights from a two-electron model system
%U http://link.aip.org/link/?JCP/125/234108/1
%V 125
%X Most applications of time-dependent density-functional theory (TDDFT)
use the adiabatic local-density approximation (ALDA) for the dynamical
exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic)
extension of the ground-state LDA into the dynamical regime leads
to a Vxc(r,t) with a memory, which causes the electron dynamics to
become dissipative. To illustrate and explain this nonadiabatic behavior,
this paper studies the dynamics of two interacting electrons on a
two-dimensional quantum strip of finite size, comparing TDDFT within
and beyond the ALDA with numerical solutions of the two-electron
time-dependent Schrödinger equation. It is shown explicitly how dissipation
arises through multiple particle-hole excitations, and how the nonadiabatic
extension of the ALDA fails for finite systems but becomes correct
in the thermodynamic limit.
@article{Ullrich2006a,
abstract = {Most applications of time-dependent density-functional theory (TDDFT)
use the adiabatic local-density approximation (ALDA) for the dynamical
exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic)
extension of the ground-state LDA into the dynamical regime leads
to a Vxc(r,t) with a memory, which causes the electron dynamics to
become dissipative. To illustrate and explain this nonadiabatic behavior,
this paper studies the dynamics of two interacting electrons on a
two-dimensional quantum strip of finite size, comparing TDDFT within
and beyond the ALDA with numerical solutions of the two-electron
time-dependent Schrödinger equation. It is shown explicitly how dissipation
arises through multiple particle-hole excitations, and how the nonadiabatic
extension of the ALDA fails for finite systems but becomes correct
in the thermodynamic limit.},
added-at = {2010-01-22T12:15:18.000+0100},
author = {Ullrich, C. A.},
biburl = {https://www.bibsonomy.org/bibtex/29af53adc75beabf37517b8d9c4e3acd3/myrta},
description = {Time dependent density functional theory; Memory effects kernel; breakdown adiabatic approximation},
doi = {10.1063/1.2406069},
eid = {234108},
file = {:home/cfc/myrta/VirtualLibrary/MemoryKernel/JChemPhys_125_234108.pdf:PDF},
interhash = {075d60d6fa24ddb7f631afdf9c8f8335},
intrahash = {9af53adc75beabf37517b8d9c4e3acd3},
journal = {The Journal of Chemical Physics},
keywords = {Schrodinger correlations density electron equation; functional ground states; theory;},
number = 23,
numpages = {10},
pages = 234108,
publisher = {AIP},
review = {Nice Intro/Review on relaxation/dissipation effects
2 el in a 2D quantum strip of finite length L
Exact Solution vs ALDA and ALDA+M (memory) TD evolution
The dipole moment in ALDA and exact solution oscillates at the frequency,
only in the exact a beat is visible due to the coupling between single
and double excitations.
Within TD-KS this effect has to be reproduced by the non-adiabacity
of the xc potential. The non adiabatic part of the potential will
act as a dissipative force.
ALDA+M may be fine as non adiabatic approximation for infinite system,
but for finite systems produce artificial dissipative effects due
to the unphysical coupling to continua of multi particle-hole excitations
that are implicitly contained in hom el liquid
For a non finite systems: extrapolation for L->\infty: the beat oscillation
wavelenght is proportional to L, if L goes to infinity the beat oscillation
becomes a "dissipation"
NB Energy is always conserved, so (at least in finite system) there
is a trasfer of energy between two sets of electronic degrees of
freedom coupled trough Coulombic},
timestamp = {2010-01-22T12:15:23.000+0100},
title = {Time-dependent density-functional theory beyond the adiabatic approximation:
Insights from a two-electron model system},
url = {http://link.aip.org/link/?JCP/125/234108/1},
volume = 125,
year = 2006
}