A theory of nonequilibrium steady states in quantum chaotic systems. (25th September 2017) - Wang, Pei
Abstract: Nonequilibrium steady state (NESS) is a quasistationary state, in which exist currents that continuously produce entropy, but the local observables are stationary everywhere. We propose a theory of NESS under the framework of quantum chaos. In an isolated quantum system whose density matrix follows a unitary evolution, there exist initial states for which the thermodynamic limit and the long-time limit are noncommutative. The density matrix ρ ^ of these states displays a universal structure. Suppose that | α ⟩ and | β ⟩ are different eigenstates of the Hamiltonian with energies E α and E β, respectively. ⟨ α | ρ ^ | β ⟩ behaves as a random number which has zero mean. In thermodynamic limit, the variance of ⟨ α | ρ ^ | β ⟩ is a smooth function of | E α − E β |, scaling as 1 / | E α − E β | 2 in the limit | E α − E β | → 0 . If and only if this scaling law is obeyed, the initial state evolves into NESS in the long time limit. We present numerical evidence of our hypothesis in a few chaotic models. Furthermore, we find that our hypothesis indicates the eigenstate thermalization hypothesis (ETH) for current operators in a bipartite system.