Collective versus single-particle motion in quantum many-body systems from the perspective of an integrable model

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.

Collective vs. single-particle motion in quantum many-body systems: Spreading and its semiclassical interpretation in the perturbative regime

“…We are mainly interested in self-bound systems such as nuclei, where unlike Bose-Einstein condensates no external confining potential is needed. It is easy to impose corresponding conditions on the matrix W which ensure that the interaction is invariant under translations and that the system is bounded [7]. We now couple the two chains by an interaction which depends on the differences between their coordinates,…”

“…and M is a diagonal matrix whose elements read [7] M ij = δ ij l K il . Note that both matrices W + M ± K are symmetric and positive (since H 0 is the Hamiltonian of a bounded system).…”

“…[7]. More precisely, K r is the (N − 1) × (N − 1) matrix obtained fromK R by deleting the first row and the first column while the vector k is the first column (excluding the first element) ofK R .…”

“…We begin with setting up our model which considerably generalizes an integrable model which we studied previously [7]. In one dimension, two chains a = 1, 2 of N interacting particles each with positions x …”

Collectivity and Periodic Orbits in a Chain of Interacting, Kicked Spins

“…Only recently, new attempts to address many-body systems in the present context were put forward, e.g. many-body localization [17][18][19] also observed in recent experiments [20,21], spreading in self-bound many-body systems [22,23], a semiclassical analysis of correlated many-particle paths in the BoseHubbard chains [24] and a trace formula connecting the energy levels to the classical many-body orbits [25,26]. There are also attempts to study field theories semiclassically [27].…”