Time-Dependent Density Functional Theory for Open Quantum Systems with Unitary Propagation

Abstract

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.

Simplified Sum-Over-States Approach for Predicting Resonance Raman Spectra. Application to Nucleic Acid Bases

“…Ultimately, the excited-state linewidths may be rigorously derived from a open-system formulation, e. g., in the framework of TDDFT. [33][34][35] In practice, the sum over electronic excited states has to be truncated. The number of excited states contributing significantly to the Raman cross sections in Eq.…”

Remarks on time-dependent [current]-density functional theory for open quantum systems

“…They hold for the case where the same -A( -r, t) acts on each member of the ensemble, which coincides with the domain where the SSE is equivalent to the ME. Another verification is that our equation of motion for the current 51,53 reduces to theirs in the limit where the memory kernel is of the KL form. A proof relying on these equations of motion cannot be a proof for the Runge-Gross analog for individual trajectories in the Stochastic Schrödinger Equation.…”

“…We regard this occasion as a good opportunity to present what we believe to be an objective account of the subject. The goal of this article is to clarify our work 51,53,93 in comparison with theirs 48,49,66 in the broad context of OQS in TDDFT. The paper is structured as follows: in Section 1, we establish the notation which will be used throughout the paper, and in Section 2, we address a series of formal issues of TDDFT for OQS which have been a potential source of confusion in the literature.…”

“…[39][40][41][42][43][44][45] An alternative approach to this problem relies on Open Quantum Systems (OQS) theory, where the electronic degrees of freedom are evolved as a quantum master equation (ME), with the bath of phonons affecting the electrons via fluctuations and dissipation. [46][47][48][49][50][51][52][53][54][55] We hereby restrict the definition of OQS to the domain of systems that exchange energy-but not particles, with an environment. Scenarios where there is an actual exchange of particles between the system and the environment are beyond the scope of this article, but we refer the reader to previous investigations along these lines of thought.…”

Single molecule charge transport: from a quantum mechanical to a classical description

“…102 These dephasing terms can be handled explicitly, although there are also attempts to incorporate them directly into the system Hamiltonian in the framework of time-dependent density functional theory. 103,104 When charge transport in donor-bridge-acceptor systems is described, the additional terms that have to be included are a charge injection rate on the donor, a charge decay rate on the acceptor and dephasing rates g on bridge sites. The latter describe how much time is required for the phases of the charge carrier wavefunction at different atoms in a molecule to lose correlation, which makes components of the wavefunction travelling along different spatial pathways incoherent and the charge transport, by definition, classical.…”