{
  "id": "2109.00425",
  "version": "v1",
  "published": "2021-09-01T15:17:18.000Z",
  "updated": "2021-09-01T15:17:18.000Z",
  "title": "Non-Boltzmann/Gibbs Distribution for Non-Hermitian Steady States at Finite Temperature",
  "authors": [
    "Qian Du",
    "Kui Cao",
    "Su-Peng Kou"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The Boltzmann/Gibbs distribution is a fundamental concept in statistical physics that governs the distribution of different equilibrium states at a particular temperature. For non-Hermitian (NH) systems at finite temperature, the equilibrium state becomes a steady state and the Boltzmann/Gibbs distribution is deformed. In this paper we showed a universal feature for NH steady states at finite temperature -- the non-Boltzmann/Gibbs distribution. To make it clear, we took a two-level NH systems as an example and developed the quantum Liouvillian statistical theory to characterize it. The density matrix for the two-level NH system at finite temperature is effectively described by that for a two-level Hermitian system with certain Liouvillian Hamiltonian. In particular, according to the non-Boltzmann/Gibbs distribution, non-thermalization effect for steady states at high temperature was explored that is quite different from thermalization effect for usual equilibrium states in Hermitian systems. This discovery will open a door to novel physics for NH systems at finite temperature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-01T15:17:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite temperature",
      "non-hermitian steady states",
      "non-boltzmann/gibbs distribution",
      "two-level nh system",
      "hermitian system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}