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Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise

Michele Coppola*

  • *Contact author: michele.coppola@ijs.si
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Phys. Rev. B 112, 024315 – Published 25 July, 2025

DOI: https://doi.org/10.1103/29z8-3t16

Abstract

The mean-state dynamics of free fermions subject to random projective measurements of local occupation number operators is governed by a Lindblad equation with dephasing noise. In the continuum limit, the equation of motion for the correlation matrix is mapped to a kinetic equation for the Wigner function, which corresponds to a special case of the Bhatnagar-Gross-Krook (BGK) equation without energy conservation. Our main result is the solution to the kinetic equation, showing that the Wigner dynamics emerges from stochastic sampling of classical run-and-tumble processes. As an application, we recover the crossover between ballistic and diffusive transport regimes.

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Phys. Rev. B 112, 024315– Published 25 July, 2025
  • Received 24 January 2025
  • Revised 20 June 2025
  • Accepted 9 July 2025
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