Dynamics in Quantum Statistical Mechanics

R. Balescu

William C. Schieve, Lawrence Paul Horwitz

Ian D. Lawrie

The relationship between two approaches to the study of non-equilibrium field theories, namely quantum statistical mechanics and thermo field dynamics, is investigated. The formalism of superoperators acting in the Liouville space of density matrices is used to provide a detailed translation between the two approaches. It is found that thermo field dynamics is exactly equivalent to a restricted version of quantum statistical mechanics, in which the initial density matrix is constrained to be Gaussian. The dissipative perturbation theory developed within thermo field dynamics is translated into the language of statistical mechanics, and is found to be equivalent to that devised by the author using the statistical-mechanical closed-time-path method, except that the latter theory is not restricted to Gaussian initial states.

David Wallace

I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations governing particular degrees of freedom). I contrast these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics; in this last case, I argue that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. Along the way various foundational issues in statistical and quantum physics are (hopefully!) illuminated.

Massimo V. Fischetti, William G. Vandenberghe

Carl S. Helrich