Statistical mechanics of one-dimensional quantum droplets
- URL: http://arxiv.org/abs/2102.12932v3
- Date: Fri, 17 Sep 2021 00:56:04 GMT
- Title: Statistical mechanics of one-dimensional quantum droplets
- Authors: T. Mithun, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
- Abstract summary: We study the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets.
We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions.
- Score: 0.0
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: We study the statistical mechanics and the dynamical relaxation process of
modulationally unstable one-dimensional quantum droplets described by a
modified Gross-Pitaevskii equation. To determine the classical partition
function thereof, we leverage the semi-analytical transfer integral operator
(TIO) technique. The latter predicts a distribution of the observed wave
function amplitudes and yields two-point correlation functions providing
insights into the emergent dynamics involving quantum droplets. We compare the
ensuing TIO results with the probability distributions obtained at large times
of the modulationally unstable dynamics as well as with the equilibrium
properties of a suitably constructed Langevin dynamics. We find that the
instability leads to the spontaneous formation of quantum droplets featuring
multiple collisions and by which are found to coalesce at large evolution
times. Our results from the distinct methodologies are in good agreement aside
from the case of low temperatures in the special limit where the droplet
widens. In this limit, the distribution acquires a pronounced bimodal
character, exhibiting a deviation between the TIO solution and the Langevin
dynamics.
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