The paper derives the exact Wigner-function propagator for a BGK-type kinetic equation with dephasing noise, showing it equals the probability density of classical run-and-tumble particles with uniformly randomized momenta.
Some speculations about local thermalization of nonequilibrium extended quantum systems
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abstract
We discuss the possibility of defining an emergent local temperature in extended quantum many-body systems evolving out of equilibrium. For the most simple case of free-fermionic systems, we give an explicit formula for the effective temperature in the case of, not necessarily unitary, Gaussian preserving dynamics. In this framework, we consider the hopping fermions on a one-dimensional lattice submitted to randomly distributed projective measurements of the local occupation numbers. We show from the average over many quantum trajectories that the effective temperature relaxes exponentially towards infinity.
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Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
The paper derives the exact Wigner-function propagator for a BGK-type kinetic equation with dephasing noise, showing it equals the probability density of classical run-and-tumble particles with uniformly randomized momenta.