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

2009/11/13 by Jens Hammerling, Jens Hämmerling, Hammerling, Jens +4
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #nlin.CD #quant-ph

paper · pdf · doi:10.48550/arxiv.0911.2724

20 pages, 1 figure

arxiv created 2009/11/13 · openalex publication_date 2009/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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