%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 }