The dynamics of the open Bose gas
This article provides a rigorous treatment of the dynamics of Bose- Einstein condensation. In the first part of their paper, the authors, starting from first principles, give a derivation of the kinetic equation describing a gas of Bosons interacting with a heat bath. This non-linear integro-differential equation is then analyzed. First, the global existence and uniqueness of the solution is established. Next, the asymptotic properties of the solution are studied in great detail. The rate of approach to equilibrium is related to the spectral gap of a certain operator, and shows a qualitative change of the critical density. This provides a rigorous microscopic foundation for the phenomenon of critical showing down, so often advocated on purely heuristic bases. Finally, the behaviour of the model is compared to the predictions of the various existing phenomenological theories. An extension of this work can be found in [the authors, Ann. Inst. Henri Poincaré, Anal. Non- Linéaire 1, 413 (1984)].
non-linear integro- differential equation
global existence and uniqueness of the solution
scientific article; zbMATH DE number 3868039
scientific article