Fröhlich, Jürg and Gang, Zhou (2014) Emission of Cherenkov radiation as a mechanism for Hamiltonian friction. Advances in Mathematics, 264 . pp. 183-235. ISSN 0001-8708. doi:10.1016/j.aim.2014.07.013. https://resolver.caltech.edu/CaltechAUTHORS:20141009-081458884
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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 ∞.
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| 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. | ||||||||||||
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| Subject Keywords: | Cherenkov radiation; Fermi golden rules; Supersonic classical particle; Bose Einstein condensate; Quantum friction | ||||||||||||
| DOI: | 10.1016/j.aim.2014.07.013 | ||||||||||||
| Record Number: | CaltechAUTHORS:20141009-081458884 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20141009-081458884 | ||||||||||||
| Official Citation: | Jürg Fröhlich, Zhou Gang, Emission of Cherenkov radiation as a mechanism for Hamiltonian friction, Advances in Mathematics, Volume 264, 20 October 2014, Pages 183-235, ISSN 0001-8708, http://dx.doi.org/10.1016/j.aim.2014.07.013. (http://www.sciencedirect.com/science/article/pii/S000187081400245X) | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 50293 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 09 Oct 2014 21:26 | ||||||||||||
| Last Modified: | 10 Nov 2021 18:54 |
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