Abstract
We discuss the transport of a tracer particle through the Bose–Einstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (‘mean-field limit’), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ‘Hamiltonian friction’. It is also of interest in connection with the phenomenon of ‘decoherence’ in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.
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References
W De Roeck and J Fröhlich, Commun. Math. Phys. 303(3), 613 (2011)
W De Roeck, J Fröhlich and K Schnelli, paper to appear
D Egli and Z Gang, Some Hamiltonian models of friction ii, arXiv:1108.5545 (2011)
J Fröhlich, Z Gang and A Soffer, Friction in a model of Hamiltonian dynamics, arXiv:1110.6550 (2011)
J Fröhlich, Z Gang and A Soffer, J. Math. Phys. 52, 083508 (2011)
D Egli, J Fröhlich, Z Gang and I M Sigal, paper in preparation
L Bruneau and S De Bièvre, Commun. Math. Phys. 229(3), 511 (2002)
S Caprino, C Marchioro and M Pulvirenti, Commun. Math. Phys. 264(1), 167 (2006)
D L Kovrizhin and L A Maksimov, Phys. Lett. A282(6), 421 (2001)
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“A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion.” (Aristotle)
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FRÖHLICH, J., GANG, Z. On the theory of slowing down gracefully. Pramana - J Phys 78, 865–874 (2012). https://doi.org/10.1007/s12043-012-0313-6
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DOI: https://doi.org/10.1007/s12043-012-0313-6