From Interacting Particles to Equilibrium Statistical Ensembles

TL;DR

This paper presents a particle-based framework for understanding equilibrium states in isolated quantum systems, especially integrable models, clarifying the role of mode occupations and generalized ensembles.

Contribution

It introduces a particle-centric formulation for equilibrium ensembles in integrable models, linking generalized Gibbs ensembles to mode occupation numbers and resolving previous conceptual gaps.

Findings

Mode occupation numbers are essential for describing equilibrium in integrable models.

Generalized Gibbs ensembles can be interpreted through particle mode occupations.

Explicit examples demonstrate the effectiveness of the particle-based approach.

Abstract

We argue that a particle language provides a conceptually simple framework for the description of anomalous equilibration in isolated quantum systems. We address this paradigm in the context of integrable models, which are those with particles that are stable against decay. In particular, we demonstrate that a complete description of equilibrium ensembles for interacting integrable models requires a formulation built from the mode occupation numbers of the underlying particle content, mirroring the case of non-interacting particles. This yields an intuitive physical interpretation of generalized Gibbs ensembles, and reconciles them with the microcanonical ensemble. We explain how previous attempts to identify an appropriate ensemble overlooked an essential piece of information, and provide explicit examples in the context of quantum quenches.