# Probing the eigenstates thermalization hypothesis with many-particle quantum walks on lattices

## TL;DR

This paper demonstrates that many-particle quantum walks on lattices exhibit thermalization behavior similar to Hamiltonian dynamics, with entropy and temperature relaxing to a quantum thermal state.

## Contribution

It provides a computational proof that discrete quantum walks can model thermalization phenomena in many-particle systems, extending understanding of quantum statistical mechanics.

## Key findings

- Vertices counting statistics relax to a steady state.
- Temperature of configurations stabilizes during dynamics.
- Effective Hilbert space dimension remains relaxed after thermalization.

## Abstract

We simulate dynamics of many-particle systems of bosons and fermions using discrete time quantum walks on lattices. We present a computational proof of a behavior of the simulated systems similar to the one observed in Hamiltonian dynamics during quantum thermalization. We record the time evolution of the entropy and the temperature of a specific particle configuration during the entire dynamics and observe how they relax to a state we call quantum walks thermal state. This observation is made on two types of lattices while simulating different numbers of particles walking on two grid graphs with 25 vertices. In each case, we observe that the vertices counting statistics, the temperature of the indexed configuration and the dimension of the effective configuration Hilbert space relax simultaneously and remain relaxed for the rest of the many-particle quantum walks.