Communications in Mathematical Physics

, Volume 315, Issue 2, pp 401–444 | Cite as

Friction in a Model of Hamiltonian Dynamics

  • Jürg Fröhlich
  • Zhou Gang
  • Avy Soffer


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


Banach Space Tracer Particle Decay Estimate Hamiltonian Dynamics Heuristic Idea 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bruneau L., De Bièvre S.: A Hamiltonian model for linear friction in a homogeneous medium. Commun. Math. Phys. 229, 511–542 (2002)ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Caprino S., Marchioro C., Pulvirenti M.: Approach to equilibrium in a microscopic model of friction. Commun. Math. Phys. 264, 167–189 (2006)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    Egli, D., Gang, Z.: Some Hamiltonian models of friction II, Submitted, available at [math-ph], 2011
  4. 4.
    Fröhlich, J., Gang, Z., Soffer, A.: Some Hamiltonian models of friction, J. Math. Phys. 52, 083508 (2011), selected for September 2011 issue of Virtual Journal of Atomic Quantum FluidsGoogle Scholar
  5. 5.
    Fröhlich, J., Sigal, I.M., Soffer, A., Gang, Z.: In preparationGoogle Scholar
  6. 6.
    Imaykin V., Komech A., Spohn H.: Scattering asymptotics for a charged particle coupled to the Maxwell field. J. Math. Phys. 52, 042701 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Kovrizhin D., Maksimov L.: “Cherenkov radiation” of a sound in a Bose condensed gas. Phys. Lett. A 282, 421–427 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    Spohn, H.: Dynamics of Charged Particles and Their Radiation Field. Cambridge: Cambridge University Press, 2004Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute for Theoretical Physics, ETH ZurichZürichSwitzerland
  2. 2.Department of MathematicsRutgers UniversityNew JerseyUSA

Personalised recommendations