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Ballistic motion of a tracer particle coupled to a Bose gas

Fröhlich, Jürg and Gang, Zhou (2014) Ballistic motion of a tracer particle coupled to a Bose gas. Advances in Mathematics, 259 . pp. 252-268. ISSN 0001-8708. https://resolver.caltech.edu/CaltechAUTHORS:20140605-091845264

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Abstract

We study the motion of a heavy tracer particle weakly coupled to a dense interacting Bose gas exhibiting Bose–Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We derive the effective dynamics of the tracer particle, which is described by a non-linear integro-differential equation with memory, and prove that if the initial speed of the tracer particle is below the speed of sound in the Bose gas the motion of the particle approaches an inertial motion at constant velocity at large times.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1302.0429arXivDiscussion Paper
http://dx.doi.org/10.1016/j.aim.2014.03.014DOIArticle
http://www.sciencedirect.com/science/article/pii/S000187081400108XPublisherArticle
Additional Information:© 2014 Elsevier Inc. Received 7 February 2013; Accepted 10 March 2014; Available online 3 April 2014. Communicated by Charles Fefferman. We are indebted to Daniel Egli, Arick Shao and Israel Michael Sigal for numerous very illuminating discussions. Our collaboration on the problems solved in this paper has been made possible by a stay at the Institute for Advanced Study in Princeton. We wish to thank our colleagues and the staff at the Institute for hospitality. Z.G. would like to thank the Mathematics Department of the University of Illinois at Urbana Champaign for hospitality when the work was done. The stay of J.F. at IAS has been supported by ‘The Fund for Math’ and ‘The Monell Foundation’.
Funders:
Funding AgencyGrant Number
Fund for MathUNSPECIFIED
Monell FoundationUNSPECIFIED
Subject Keywords:Tracer particle; Bose-Einstein condensation; Cerenkov radiation
Record Number:CaltechAUTHORS:20140605-091845264
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140605-091845264
Official Citation:Jürg Fröhlich, Zhou Gang, Ballistic motion of a tracer particle coupled to a Bose gas, Advances in Mathematics, Volume 259, 10 July 2014, Pages 252-268, ISSN 0001-8708, http://dx.doi.org/10.1016/j.aim.2014.03.014. (http://www.sciencedirect.com/science/article/pii/S000187081400108X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46091
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jun 2014 18:24
Last Modified:03 Oct 2019 06:40

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