Quantum transport theory.

Abstract

Within the framework of the quantum transport theory based on the Wigner transform of the density matrix I study first in non-relativistic and subsequently in relativistic formulation a number of applications. I also develop further the recently proposed relativistic theory: the classical limit is carefully derived and the integral equations of the relativistic Wigner function derived explicitly. I show how it is possible to obtain the Schwinger like particle production rate from relativistic quantum transport equations. Noteworthy numerical results address the shape of the relativistic Wigner function of a given quantum state. Other numerical studies are primarily oriented towards the time evolution of the Wigner function--I can presently solve only the nonrelativistic case in which there is no mixing between particle production and flow phenomena: I consider numerically the fate of the muon after muon catalyzed fusion.