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Non-linear transport in an out-of-equilibrium single-site Bose Hubbard model: scaling, rectification and time dynamics

Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-Reservoir system, namely, the single-site Bose-Hubbard model coupled to two reservoirs at different temperatures. Using Redfield equations in Born-Markov approximation, we compute non-equilibrium average particle number, energy and currents beyond linear response regime, both time-dynamics and steady state and investigate its dependence on various tunable parameters analytically. We find interesting scaling laws in high temperature regimes that are independent of choice of bath spectral functions. We also demonstrate that the system shows very interesting particle and energy current rectification properties which can be controlled via the relative strength of interaction and temperatures, as well as via the degree of asymmetry in system-bath coupling. Specifically, we find inversion of direction of thermal rectification as a function of the relative strength of the interaction strength and the temperatures. We also show that, in the limit of low-temperature and high interaction strength our results are consistent with the non-equilibrium spin-Boson model. Our results are experimentally relevant not only to hybrid quantum systems, but also in other areas such as molecular junctions.