Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-03-19
J. Phys. A: Math. Theor. 43 (2010) 403001
Physics
Condensed Matter
Statistical Mechanics
52 pages, 4 figures; to appear in J. Phys. A: Math. Theor
Scientific paper
10.1088/1751-8113/43/40/403001
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.
Kriecherbauer Thomas
Krug Joachim
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