1. Searching for the Tracy-Widom distribution in nonequilibrium processes.
- Author
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Mendl, Christian B. and Spohn, Herbert
- Subjects
- *
GAUSSIAN processes , *DISTRIBUTION (Probability theory) , *THERMODYNAMIC equilibrium , *MATHEMATICAL physics , *THEORY of wave motion - Abstract
While originally discovered in the context of the Gaussian unitary ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters, the profile develops a rarefaction wave while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam type anharmonic chain, we will demonstrate that the time-integrated current has a deterministic contribution, linear in time t, and fluctuations of size t1/3 with a Tracy-Widom distributed random amplitude. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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