Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions

TL;DR

This paper extends static duality between 1-D Bosons and Fermions to dynamical scenarios, revealing dualities in non-equilibrium work distributions and showing classical limits where different models converge.

Contribution

It introduces a dynamical duality for non-equilibrium work distributions in 1-D interacting bosonic and fermionic systems, including numerical validation.

Findings

Work distributions are dual between Lieb-Liniger and Cheon-Shigehara models.

Tonks-Girardeau gas work distribution matches that of free fermions.

Classical limit leads to convergence of work distributions across models.

Abstract

We extend the well-known static duality \cite{girardeau1960relationship, cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version. By utilizing this dynamical duality we find the duality of non-equilibrium work distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau (TG) gas is identical to that of 1-D free fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1-D noninteracting distinguishable particles, although their elemetary excitations (quasi-particles) obey different statistics, e.g. the Bose-Einstein, the Fermi-Dirac and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.