Abstract
The evolution of a quantum system towards thermal equilibrium is usually studied by approximate methods, which have their limits of validity and should be checked against analytically solvable models. In this paper, we propose an analytically solvable model to investigate the energy transfer between a bosonic bath and a fermionic chain which are nonlinearly-coupled to each other. The bosonic bath consists of an infinite collection of non-interacting bosonic modes, while the fermionic chain is represented by a chain of interacting fermions with nearest-neighbor interactions. We compare behaviors of the temperature-dependent energy current J_T and temperature-independent energy current J_TI for different bath configurations. With respect to the bath spectrum, J_T decays exponentially for Lorentz-Drude type bath, which is the same as the conventional approximations. On the other hand, the decay rate is 1/t³ for Ohmic type and 1/t for white noise, which doesn't have conventional counterparts. For the temperature-independent current J_TI, the decay rate is divergent for the Lorentz-Drude type bath, 1/t⁴ for the Ohmic bath, and 1/t for the white noise. When further considering the dynamics of the fermionic chain, the current will be modulated based on the envelope from the bath. As an example, for a bosonic bath with Ohmic spectrum, when the fermionic chain is uniformly-coupled, we have J_T∝1/t⁶ and J_TI∝1/t³. Remarkably, for perfect state transfer (PST) couplings, there always exists an oscillating quantum energy current J_TI. Moreover, it is interesting that J_T is proportional to (N-1)^1/2 at certain times for PST couplings under Lorentz-Drude or Ohmic bath.