Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle

TL;DR

This paper explores the dynamics of quantum walks involving distinguishable and indistinguishable particles, revealing how many-particle systems can mimic single-particle behavior, enable state separation, and exhibit localization effects.

Contribution

It introduces analysis of many-particle quantum walks, including distinguishable and indistinguishable particles, and demonstrates localization and state separation phenomena.

Findings

Many-particle density profiles redistribute over time.

Collective evolution resembles single-particle quantum walks.

Two-particle localization at the lattice center.

Abstract

We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle system resembles the single-particle quantum walk evolution when the number of steps is greater than the number of particles in the system. For non-uniform initial states we show that the quantum walks can be effectively used to separate the basis states of the particle in position space and grouping like state together. We also discuss a two-particle quantum walk on a two- dimensional lattice and demonstrate an evolution leading to the localization of both particles at the center of the lattice. Finally we discuss the outcome of a quantum walk of two indistinguishable particles interacting at some point during the evolution.