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Exact quantum transport in non-Markovian open Gaussian systems

Guglielmo Pellitteri1,*, Vittorio Giovannetti1,2,†, and Vasco Cavina1,‡

  • *Contact author: guglielmo.pellitteri@sns.it
  • †Contact author: vittorio.giovannetti@sns.it
  • ‡Contact author: vasco.cavina@sns.it
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Phys. Rev. B 114, 144308 – Published 28 September, 2026

DOI: https://doi.org/10.1103/577j-lrhg

Abstract

We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-Büttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of nontrivial out-of-equilibrium dynamics.

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Phys. Rev. B 114, 144308– Published 28 September, 2026
  • Received 21 April 2026
  • Revised 6 July 2026
  • Accepted 9 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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