Collective versus Single--Particle Motion in Quantum Many--Body Systems: Spreading and its Semiclassical Interpretation

TL;DR

This paper investigates the relationship between collective and single-particle motions in quantum many-body systems, demonstrating a universal semiclassical interpretation of collective excitations through a renormalization approach.

Contribution

It introduces a renormalization method that maps a complex quantum system to a Caldeira-Leggett model, revealing a universal semiclassical interpretation of collective excitations.

Findings

Spectral density always admits a semiclassical interpretation

Renormalization maps the system to a Caldeira-Leggett-type model

Universal behavior in collective excitation spectra

Abstract

We study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction, we calculate the spectral density for collective excitations. We obtain the remarkable result that it always has a unique semiclassical interpretation. We show this by a proper renormalization procedure which allows us to map our system to a Caldeira-Leggett--type of model in which the bath is part of the system.