Collective versus Single--Particle Motion in Quantum Many--Body Systems from the Perspective of an Integrable Model

TL;DR

This paper investigates how collective motion emerges in an integrable quantum system of coupled oscillators, revealing a damped harmonic oscillator behavior and linking quantum transition strengths to classical dynamics.

Contribution

It introduces a novel mapping of an integrable oscillator system onto a Caldeira-Leggett type model with an internal bath, elucidating collective dynamics in quantum many-body systems.

Findings

The collective coordinate behaves as a damped harmonic oscillator.

Quantum transition strengths are governed by classical dynamics.

The bath of phonons is an intrinsic part of the system, not an external environment.

Abstract

We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.