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Stochastic integral representation for the dynamics of disordered systems

Ivana Kurečić*

Tobias J. Osborne†

  • Max Planck Institute of Quantum Optics, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany and Munich Center for Quantum Science and Technology, Schellingstrasse 4, D-80799 Munich, Germany

  • Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany

  • *ivanakurecic@gmail.com
  • †tobias.osborne@itp.uni-hannover.de
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Phys. Rev. A 107, 042213 – Published 17 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042213

Abstract

The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Itô stochastic calculus is obtained. The stochastic integral representation affords many advantages, including amenability to analytic approximation, potential applicability to interacting systems, and compatibility with tensor network methods. The integral may be expanded to produce a series of approximations, the first of which already includes all diffusive corrections and, further, is manifestly completely positive. The addition of fluctuations leads to a convergent series of systematic corrections. As examples, expressions for the density of states and spectral form factor for the Anderson model are obtained.

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Phys. Rev. A 107, 042213– Published 17 April, 2023
  • Received 7 November 2022
  • Accepted 23 March 2023
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