Canonical description of 1D few-body systems with short range interaction

TL;DR

This paper develops a canonical framework combining cluster expansions and dynamical information to analyze 1D few-body systems with short-range interactions, revealing universal integrability properties.

Contribution

It introduces a novel analytical approach that overcomes limitations of virial expansions, accurately capturing thermodynamics and spectra of 1D few-body quantum systems.

Findings

Excellent agreement with numerical simulations

Universal behavior of interaction effects

Analytical expressions for thermodynamic properties

Abstract

We address the fundamental interplay between indistinguishability and interactions when discreteness effects are neglected in systems with strictly fixed number of particles. For this end we supplement cluster expansions (many-body canonical techniques where quantum statistics is treated exactly) with short-time/large volume dynamical information where interparticle forces are described non-perturbatively. This approach, specially suitable for the few-body case where it overcomes the inappropriate use of virial expansions, can be consistently combined with scaling considerations, minimal ground-state information and strong coupling expansions in such a way that a single interaction event provides most of the thermodynamic and spectral properties of 1D systems with short range interactions. Our analytical results, in excellent agreement with numerical simulations, show a form of universal integrability of interaction effects for arbitrary confinements.