{
  "id": "2211.01755",
  "version": "v1",
  "published": "2022-11-03T12:37:54.000Z",
  "updated": "2022-11-03T12:37:54.000Z",
  "title": "KMS states and their classical limit",
  "authors": [
    "Christiaan J. F. van de Ven"
  ],
  "comment": "39 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A continuous bundle of $C^*$-algebras provides a rigorous framework to study the thermodynamic limit of quantum theories. If the bundle admits the additional structure of a strict deformation quantization (in the sense of Rieffel) one is allowed to study the classical limit of the quantum system, i.e. a mathematical formalization in which convergence of algebraic quantum states to probability measures on phase space (typically a Poisson or symplectic manifold) is studied. In this manner we first prove the existence of the classical limit of Gibbs states illustrated with a class of Schr\\\"{o}dinger operators in the regime where Planck's constant $\\hbar$ appearing in front of the Laplacian approaches zero. We additionally show that the ensuing limit corresponds to the unique probability measure satisfying the so-called classical or static KMS- condition. Subsequently, a similar study is conducted for the free energy in the classical limit of mean-field quantum spin systems in the regime of large particles, and the existence of the classical limit of the relevant Gibbs states is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-03T12:37:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical limit",
      "kms states",
      "mean-field quantum spin systems",
      "unique probability measure",
      "laplacian approaches zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}