Published October 20, 2014
| Version Submitted
Journal Article
Open
Emission of Cherenkov radiation as a mechanism for Hamiltonian friction
Abstract
We study the motion of a heavy tracer particle weakly coupled to a dense, weakly 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 prove that if the initial speed of the tracer particle is above the speed of sound in the Bose gas, and for a suitable class of initial states of the Bose gas, the particle decelerates due to emission of Cherenkov radiation of sound waves, and its motion approaches a uniform motion at the speed of sound, as time t tends to ∞.
Additional Information
© 2014 Elsevier Inc. Received 25 November 2013; Accepted 11 July 2014; Available online 24 July 2014. Communicated by Charles Fefferman. We are indebted to Daniel Egli, Burak Erdogan, Eduard Kirr, Nikolas Tzirakis and, especially, to 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 col-leagues at the School of Mathematics, in particular Thomas C. Spencer, and the staff of the Institute for hospitality. The stay of Jürg Fröhlichat IAS has been supported by 'The Fund for Math' and 'The Robert and Luisa Fernholz Visiting Professorship Fund'. The research of Zhou Gang was partly supported by NSF grant DMS-1308985.Attached Files
Submitted - 1311.6377v2.pdf
Files
1311.6377v2.pdf
Additional details
Identifiers
- Eprint ID
- 50293
- Resolver ID
- CaltechAUTHORS:20141009-081458884
Related works
- Describes
- http://arxiv.org/abs/1311.6377 (URL)
Funding
- Fund for Math
- Robert and Luisa Fernholz Visiting Professorship Fund
- NSF
- DMS-1308985
Dates
- Created
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2014-10-09Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field