{
  "id": "2105.09575",
  "version": "v1",
  "published": "2021-05-20T08:00:01.000Z",
  "updated": "2021-05-20T08:00:01.000Z",
  "title": "Time correlation functions for quantum systems: the case of harmonic oscillators",
  "authors": [
    "Vladislav Efremkin",
    "Jean-Louis Barrat",
    "Stefano Mossa",
    "Markus Holzmann"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The quantum harmonic oscillator represents the most common fundamental building block to compute thermal properties of virtually any dielectric crystalline material at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even disordered solids. In general, Path Integral Monte Carlo (PIMC) methods provide a powerful numerical tool to stochastically determine thermodynamic quantities without systematic bias, not relying on perturbative schemes. Addressing transport properties, for instance the calculation of thermal conductivity from PIMC, however, has turned out to be substantially more difficult. Although correlation functions of current operators can be determined by PIMC in the form of analytic continuation on the imaginary time axis, Bayesian methods are usually employed for the numerical inversion back to real-time response functions. This task not only relies strongly on the accuracy of the PIMC data, but also introduces noticeable dependence on the underlying model used for the inversion problem. Here, we address both difficulties with great care. In particular, we first devise improved estimators for current correlations which substantially reduce the variance of the PIMC data. Next, we provide a neat statistical approach to the inversion problem, blending into a fresh workflow the classical stochastic maximum entropy method together with more recent notions borrowed from statistical learning theory. We test our ideas on a single harmonic oscillator and a collection of oscillators with a continuous distribution of frequencies, establishing solid grounds for an unbiased, fully quantum mechanical calculation of transport properties in solids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-20T08:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time correlation functions",
      "quantum systems",
      "path integral monte carlo",
      "transport properties",
      "inversion problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}