Nonequilibrium steady state in open quantum systems: Influence action, stochastic equation and power balance

摘要: Abstract The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is fundamental subject main theme research in statistical mechanics decades. For Gaussian systems, such as chain classical harmonic oscillators connected at each end to heat bath, anharmonic under specified conditions, definitive answers exist the form proven theorems. Answering this question quantum many-body poses challenge present. In work we address issue by deriving stochastic equations reduced system with self-consistent backaction from two baths, calculating energy flow one bath other exhibiting power balance relation total (chain + baths) which testifies NESS late times. Its insensitivity initial conditions corroborates its uniqueness. functional method adopt here entails use influence functional, coarse-grained effective actions, can derive calculate average values physical variables open systems. This involves both taking expectation operators distributional averages stemming environment. though formal appearance compact complete. It also easily accommodate perturbative techniques diagrammatic methods field theory. Taken all together it provides solid platform carrying out systematic investigations into dynamics thermodynamics.