Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A theory of nonequilibrium steady states in quantum chaotic systems (1607.05231v2)

Published 18 Jul 2016 in cond-mat.stat-mech, cond-mat.mes-hall, and quant-ph

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, there exist some initial states for which the thermodynamic limit and the long-time limit are noncommutative. The density matrix $\hat \rho$ of these states displays a universal structure. Suppose that $\alpha$ and $\beta$ are different eigenstates of the Hamiltonian with energies $E_\alpha$ and $E_\beta$, respectively. $<\alpha|\hat \rho|\beta>$ behaves as a random number which approximately follows the Laplace distribution with zero mean. In thermodynamic limit, the variance of $<\alpha|\hat \rho|\beta>$ is a smooth function of $\left|E_\alpha-E_\beta\right|$, scaling as $1/(E_\alpha-E_\beta)2$ in the limit $\left|E_\alpha-E_\beta\right|\to 0$. 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 implies the eigenstate thermalization hypothesis (ETH) in a bipartite system.

Summary

We haven't generated a summary for this paper yet.