科研之友
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摘要
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 rho of these states displays a universal structure. Suppose that | alpha and | beta are di. erent eigenstates of the Hamiltonian with energies E alpha and E beta, respectively. alpha | rho | beta behaves as a random number which has zero mean. In thermodynamic limit, the variance of alpha | rho | beta is a smooth function of | E alpha -E beta |, scaling as 1/ | E alpha -E beta |(2) in the limit | E alpha -E beta | -> 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.
- 出版日期2017-9
- 单位浙江师范大学
