Abstract
When a quantum system is placed in thermal environments, we often assume that the system relaxes to the Gibbs state in which decoherence takes place in the system energy eigenbasis. However, when the coupling between the system and the environments is strong, the stationary state is not necessarily the Gibbs state due to environment-induced decoherence which can be interpreted as continuous measurement by the environments. Based on the einselection proposed by Zurek, we postulate that the Gibbs state is projected onto the pointer basis due to the continuous measurement. We justify the proposition by exact numerical simulation of a pair of coupled qubits interacting with boson gases. Furthermore, we demonstrate that heat conduction in non-equilibrium steady states can be suppressed in the strong coupling limit also by the environment-induced decoherence.
Highlights
The laws of thermodynamics and the principles of statistical mechanics tell us that every system eventually reaches a stationary state known as the Gibbs state, which is the hallmark of thermal equilibrium
For a system strongly coupled to the environments, its equilibrium state cannot be expressed with the system Hamiltonian alone, and an effective Hamiltonian based on the potential of mean force has been developed [9,10,11,12,13,14,15,16]
We tried more than ten different initial densities, and all converged to the same stationary state
Summary
The laws of thermodynamics and the principles of statistical mechanics tell us that every system eventually reaches a stationary state known as the Gibbs state, which is the hallmark of thermal equilibrium. Thermalization to the Gibbs state must involve decoherence between energy eigenstates, presumably induced by the environments surrounding the system. Such a decoherence process toward the Gibbs state has been investigated under the weak coupling limit [1]. The system density operator becomes diagonal in the pointer basis under the strong coupling limit. This einselection [18] can be considered as a consequence of continuous measurement of the system by the environment. We investigate thermalization and heat conduction in the strong coupling regime based decoherence in the pointer basis
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