Nonequilibrium statistical quantum field theory for open systems

Journal Article · Sat Apr 15 00:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.39.2253· OSTI ID:6451706

Kandrup, H E

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 rho/sub S/(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 rho/sub S/ satisfies a Liouville--von Neumann equation which implies, e.g., an isentropic evolution. Starting from ''first principles,'' i.e., the Schroedinger 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 rho/sub S/ and the ''bath'' density matrix rho/sub B/ satisfy coupled nonlinear generalizations of the Liouville--von Neumann equation and evidence a nonisentropic evolution. However, in a Vlasov-type approximation, rho/sub S/ and rho/sub B/ satisfy instead much simpler bilinear equations which imply an isentropic evolution. And finally, in the limit that the ''back reaction'' of rho/sub S/ on rho/sub B/ can be neglected in computing the evolution of rho/sub B/, one recovers a true Liouville--von Neumann equation for the evolution of rho/sub S/ in an external field.

• Research Organization: Space Astronomy Laboratory and Institute for Fundamental Theory, University of Florida, Gainesville, Florida 32609
• OSTI ID: 6451706
• Journal Information: Phys. Rev. D; (United States), Vol. 39:8
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
STATISTICAL MODELS
UNIVERSE
BOLTZMANN-VLASOV EQUATION
GRAVITATIONAL FIELDS
MEAN-FIELD THEORY
SCHROEDINGER EQUATION
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
640106* - Astrophysics & Cosmology- Cosmology
645400 - High Energy Physics- Field Theory