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Friction in a Model of Hamiltonian Dynamics

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Abstract

We study the motion of a heavy tracer particle weakly coupled to a dense ideal 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 describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle’s trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest.

“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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Authors and Affiliations

  1. Institute for Theoretical Physics, ETH Zurich, 8093, Zürich, Switzerland

    Jürg Fröhlich & Zhou Gang

  2. Department of Mathematics, Rutgers University, New Jersey, 08854, USA

    Avy Soffer

Authors
  1. Jürg Fröhlich
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  2. Zhou Gang
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  3. Avy Soffer
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Corresponding author

Correspondence to Jürg Fröhlich.

Additional information

Communicated by H. Spohn

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Fröhlich, J., Gang, Z. & Soffer, A. Friction in a Model of Hamiltonian Dynamics. Commun. Math. Phys. 315, 401–444 (2012). https://doi.org/10.1007/s00220-012-1564-2

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  • DOI: https://doi.org/10.1007/s00220-012-1564-2

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