Interacting quantum walkers: Two-body bosonic and fermionic bound states

TL;DR

This paper studies the dynamics of two interacting quantum particles, either bosons or fermions, on a lattice, focusing on their ballistic spreading and the structure of their distribution profiles.

Contribution

It introduces a detailed analysis of bound states of two particles with both hard bounds and confining potentials in quantum walks.

Findings

Bound states exhibit ballistic spreading velocities.

Asymptotic distribution profiles show multiple internal fronts.

Differences between bosonic and fermionic bound states are characterized.

Abstract

We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles has a hard bound, and the richer situation where the particles are bound by a smooth confining potential. The main emphasis is on the velocity characterizing the ballistic spreading of these bound states, and on the structure of the asymptotic distribution profile of their center-of-mass coordinate. The latter profile generically exhibits many internal fronts.