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

Abstract

Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems.Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particleparticle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.

Real‐time time‐dependent electronic structure theory

“…Ab initio real‐time time‐dependent electronic structure theory seeks to solve the time‐dependent Schrödinger equation (TDSE) for quantum systems in order to predict and simulate the response to any combination of perturbations, be they electromagnetic fields, complex environments, thermal baths, and so on. Real‐time methods have been applied to many types of spectroscopy as well as studies of coherence and charge‐transfer dynamics .…”

“…A b initio real-time time-dependent electronic structure theory seeks to solve the time-dependent Schrödinger equation (TDSE) for quantum systems in order to predict and simulate the response to any combination of perturbations, be they electromagnetic fields, [1][2][3][4][5][6][7][8][9][10][11] complex environments, [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] thermal baths, [30][31][32][33][34][35][36][37] and so on. Real-time methods have been applied to many types of spectroscopy [38][39][40][41][42][43][44][45][46][47][48][49]…”

The role of interparticle interaction and environmental coupling in a two-particle open quantum system

“…which is equivalent to consider ρ 0,0 (0) = ρ 0,1 (0) = ρ 1,0 (0) = ρ 1,1 (0) = 1 2 . This model was discussed in the context of TDDFT for open quantum systems [48,49,50,51] in Ref. [46].…”

“…. This model was discussed in the context of TDDFT for open quantum systems [56][57][58][59] in ref. 60.…”

Homogeneous Dephasing in Photosynthetic Bacterial Reaction Centers: Time Correlation Function Approach

“…As such, the photosynthetic RCs have served as a powerhouse of dynamical and structural information on quantum coherence effects, [2,3,6–13] energy‐ and electron‐transfer. Techniques such as linear (and nonlinear) molecular spectra (e. g., hole‐burning, fluorescence line narrowing (FLN), [14–22] 2‐dimensional electronic spectroscopy (2DES), [23–26] and photon echo signals), [26–29] and dispersive kinetics have been employed to probe these quantum coherence effects and hence apply to renewable energy. While the protein complexes in photosynthetic antennas exhibit variation in different species, the RCs structure seems to be similar; for example, the distribution of low‐frequency phonons ($${{\omega }_{m}\sim 20-30\ {cm}^{-1}}$$ ) in bacterial RC protein seems to be ubiquitous across different species.…”