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

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.

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…• The same result holds for the vacuum Green's functions (73) under the replacement k → k + iε and subsequent limit ε → 0: …”

“…Conversely, a quantum version of Newton's cradle constructed out of one-dimensional colliding Bose-Einstein condensates [69] showed no significant signs of thermalization, in partial contrast to a previous conjecture [70] and despite experimental noise, that is expected to foster the thermalization process. The amount of discussion [71][72][73][74] recently triggered by the observation of [69] leads to the conclusion that the understanding of the emergence of thermodynamic behavior in quantum systems is not yet fully understood -a point we will come back to within this thesis.…”

“…7, and, again, the integration extends over the volume V of the slab. The free Green's function G 0 (r − r ) is defined as in (73), V = V/µ, and…”

Spreading in integrable and non-integrable many-body systems

“…We largely use the model introduced in our previous analytical investigations [14,15]. Two clouds of interacting particles in one dimension are coupled to each other.…”

“…As we found it appropriate to slightly change some conventions of [14,15] for the numerical study, we compile all necessary formulas defining the Hamiltonian in Sec. II A.…”