Landscape, kinetics, paths and statistics of curl flux, coherence, entanglement and energy transfer in non-equilibrium quantum systems

Abstract

We develop a population and flux landscape theory for general non-equilibrium quantum systems. We illustrate our theory by modelling the quantum transport of donor-acceptor energy transfer. We find two driving forces for the non-equilibrium quantum dynamics. The symmetric part of the driving force corresponds to the population landscape contribution which mainly governs the equilibrium part of dynamics while the anti-symmetric part of the driving force generates the non-equilibrium curl quantum flux which leads to the detailed-balance-breaking and time-irreversibility. The multi-loop structure of the flux emerges forms the flux-landscape. We study the trend of changes in population and flux-landscape with respect to the voltage (temperature difference induced by environments) and electronic coupling. Improving the voltage and electronic coupling in general facilitates the quantum transport by reducing the population landscape barriers between major states and increasing the mean value of the flux. A limit-cycle mode emerges when the underlying flux-landscape becomes funnelled with a significant gap between the largest flux loop and the rest of them. On the kinetic level, we find that multiple kinetic paths between quantum states emerge and illustrate the interference effects. The degree of interference is determined by the landscape and flux. Furthermore, we quantify kinetic rate which strongly correlates with the population landscape and flux. For quantum transport, we demonstrate that as the coherence or the quantum entanglement is enhanced, the flux and energy transfer efficiency are increased. Finally it is surprising that the non-equilibriumness quantified by voltage has a non-trivial contribution on strengthening the entanglement, which is attributed to the non-local feature of the quantum curl flux.