Quebec Mathematical Sciences Colloquium

November 2, 2012 from 16:00 to 18:00 (Montreal/Miami time) On location

Dissipative motion from a Hamiltonian point of view

Colloquium presented by Jürg Fröhlich (ETH Zurich)

I will study the motion of a classical particle interacting with a dispersive wave medium. (Concretely, one may think of a heavy particle interacting with an ideal Bose gas at zero temperature, in the large-density or mean-field limit.) This is an example of a Hamiltonian system with infinitely many degrees of freedom that describes dissipative phenomena. I will show that the particle experiences a friction force with memory, which is caused by the particle's emission of Cherenkov radiation of sound waves into the medium. This friction force decelerates the particle until its speed has dropped to the minimal speed of sound in the medium (=0, for an ideal Bose gas). Various open problems that I suspect might be of interest to analysts will be described. (The results presented in this lecture have been found in joint work with Daniel Egli, Gang Zhou, Avy Soffer and Israel Michael Sigal.)

Address

Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, ROOM 6214