Numerical study of Bose–Einstein condensation in the Kaniadakis–Quarati model for bosons
File(s)
Accepted version
Author(s)
Carrillo de la Plata, Jose Antonio
Hopf, Katharina
Wolfram, Marie-Therese
Type
Journal Article
Abstract
Kaniadakis and Quarati (1994) proposed a Fokker–Planck equation with quadratic drift as a PDE model for the dynamics of bosons in the spatially homogeneous setting. It is an open question whether this equation has solutions exhibiting condensates in finite time. The main analytical challenge lies in the continuation of exploding solutions beyond their first blow-up time while having a linear diffusion term. We present a thoroughly validated timeimplicit numerical scheme capable of simulating solutions for arbitrarily long time, and thus enabling a numerical study of the condensation process in the Kaniadakis–Quarati model. We show strong numerical evidence that above the critical mass rotationally symmetric solutions of the Kaniadakis–Quarati model in 3D form a condensate in finite time and converge in entropy to the unique minimiser of the natural entropy functional. Our simulations further indicate that the spatial blow-up profile near the origin follows a universal power law and that transient condensates can occur for sufficiently concentrated initial data.
Date Issued
2020-06
Date Acceptance
2020-01-21
Citation
Kinetic and Related Models, 2020, 13 (3), pp.507-529
ISSN
1937-5093
Publisher
American Institute of Mathematical Sciences
Start Page
507
End Page
529
Journal / Book Title
Kinetic and Related Models
Volume
13
Issue
3
Copyright Statement
© American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Kinetic and Related Models following peer review. The definitive publisher-authenticated version is available online at: https://www.aimsciences.org/article/doi/10.3934/krm.2020017
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P031587/1
Subjects
Applied Mathematics
Publication Status
Published
Date Publish Online
2020-03