Thermalization of Fermionic Quantum Walkers

TL;DR

This paper studies how fermionic quantum walkers interacting with a fermionic reservoir reach thermal equilibrium, showing that their long-term behavior becomes independent of initial conditions and exhibits a flat density profile.

Contribution

It proves that under certain conditions, the sample's reduced density matrices converge to a state determined solely by the reservoir, demonstrating thermalization in a discrete fermionic quantum system.

Findings

Long-time limits of reduced density matrices depend only on the reservoir state.

Asymptotic density profile in the sample becomes flat.

Number operator correlations lose structure, indicating thermalization.

Abstract

We consider the discrete time dynamics of an ensemble of fermionic quantum walkers moving on a finite discrete sample, interacting with a reservoir of infinitely many quantum particles on the one dimensional lattice. The reservoir is given by a fermionic quasifree state, with free discrete dynamics given by the shift, whereas the free dynamics of the non-interacting quantum walkers in the sample is defined by means of a unitary matrix. The reservoir and the sample exchange particles at specific sites by a unitary coupling and we study the discrete dynamics of the coupled system defined by the iteration of the free discrete dynamics acting on the unitary coupling, in a variety of situations. In particular, in absence of correlation within the particles of the reservoir and under natural assumptions on the sample's dynamics, we prove that the one- and two-body reduced density matrices of the sample admit large times limits characterized by the state of the reservoir which are independent of the free dynamics of the quantum walkers and of the coupling strength. Moreover, the corresponding asymptotic density profile in the sample is flat and the correlations of number operators have no structure, a manifestation of thermalization.