Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-05-03
Prog. Theor. Phys. 123 (2010) 581-658
Physics
Condensed Matter
Statistical Mechanics
78 pages, 14 figures, invited paper (free access) of Prog. Theor. Phys. http://ptp.ipap.jp/link?PTP/123/581/
Scientific paper
10.1143/PTP.123.581
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Phi-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Phi-derivable approximation, i.e., an issue of how to handle the "Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy".
No associations
LandOfFree
Introduction to Nonequilibrium Statistical Mechanics with Quantum Field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Introduction to Nonequilibrium Statistical Mechanics with Quantum Field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Introduction to Nonequilibrium Statistical Mechanics with Quantum Field will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-530765