Abstract
In this article, we prove the one-to-one correspondence between vector potentials and particle and current densities in the context of master equations with arbitrary memory kernels, therefore extending time-dependent current-density functional theory (TD-CDFT) to the domain of generalized many-body open quantum systems (OQS). We also analyse the issue of A-representability for the Kohn-Sham (KS) scheme proposed by D'Agosta and Di Ventra for Markovian OQS [Phys. Rev. Lett. 2007, 98, 226403] and discuss its domain of validity. We suggest ways to expand their scheme, but also propose a novel KS scheme where the auxiliary system is both closed and non-interacting. This scheme is tested numerically with a model system, and several considerations for the future development of functionals are indicated. Our results formalize the possibility of practising TD-CDFT in OQS, hence expanding the applicability of the theory to non-Hamiltonian evolutions.
Highlights
A closed system is a quantum mechanical state that evolves under Hamiltonian evolution, obeying Schrodinger’s equation
Incorporating the open quantum systems (OQS) formalism into TD-DFT would provide a convenient set of tools for studying a vast number of dynamical processes such as excitations of molecules embedded in complex biological environments,[10] spin diffusion,[11] molecular conductance,[12] particle thermalization,[13] and many other interesting phenomena
The fact that (15) is not a continuity equation was pointed out several years ago by Frensley,[38] but has only recently been extensively studied independently by Gebauer and Car (GC)[39] and later on by Bodor and Diosi (BD).[40]
Summary
A closed system is a quantum mechanical state that evolves under Hamiltonian evolution, obeying Schrodinger’s equation. TD-DFT reformulates time-dependent quantum mechanics in terms of particle densities instead of wavefunctions (or density matrices), allowing for more affordable computational scaling than standard many-body theories when it comes to the resources needed to study the time evolution of a closed system. This constitutes the main result of our article, since we suggest switching from an interacting to a non-interacting system, and from an open to a closed system. We comment on this strategy comparing it with the previously suggested schemes, and on issues related to the development of functionals for this particular proposal.
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