Two-particle coined-quantum walk with long-range interaction

TL;DR

This paper investigates a two-particle quantum walk with long-range Coulomb-like interactions, analyzing the spectrum and molecular formations, highlighting unique effects of long-range forces on particle behavior.

Contribution

It introduces a novel two-particle quantum walk model with long-range interactions and studies its spectral properties and molecular formations based on particle statistics.

Findings

Spectrum of the system characterized

Molecular formations analyzed based on bosonic or fermionic nature

Long-range interactions affect the distinction between attractive and repulsive forces

Abstract

We present and study a two-particle quantum walk on the line in which the two particles interact via a long-range Coulombian-like interaction. We obtain the spectrum of the system as well as study the type of molecules that form, attending to the bosonic or fermionic nature of the walkers. The usual loss of distinction between attractive and repulsive forces does not entirely apply in our model because of the long-range of the interaction.