Mathematics – Dynamical Systems
Scientific paper
Apr 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..39.2253k&link_type=abstract
Physical Review D (Particles and Fields), Volume 39, Issue 8, 15 April 1989, pp.2253-2257
Mathematics
Dynamical Systems
3
Theory Of Quantized Fields, Other Topics In Statistical Physics, Thermodynamics, And Nonlinear Dynamical Systems
Scientific paper
Recently, a number of authors have begun to study the evolution of quantum fields in the early Universe characterized by a time-dependent density matrix ρS(t). All of this work is predicated on the assumption that one's ``subsystem'' of interest is in some sense ``decoupled'' from the rest of the Universe, so that ρS satisfies a Liouville-von Neumann equation which implies, e.g., an isentropic evolution. Starting from ``first principles,'' i.e., the Schrödinger equation for the totality of ``subsystem'' plus surroundings (``bath''), it is shown here how such a picture can be derived as the limiting case of a more complete statistical description. Quite generally, one finds that ρS and the ``bath'' density matrix ρB satisfy coupled nonlinear generalizations of the Liouville-von Neumann equation and evidence a nonisentropic evolution. However, in a Vlasov-type approximation, ρS and ρB satisfy instead much simpler bilinear equations which imply an isentropic evolution. And finally, in the limit that the ``back reaction'' of ρS on ρB can be neglected in computing the evolution of ρB, one recovers a true Liouville-von Neumann equation for the evolution of ρS in an external field.
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