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Searching for the Tracy-Widom distribution in nonequilibrium processes
Christian B Mendl1, Herbert Spohn2
1Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA.
Physical Review. E
|July 15, 2016
Summary
The Tracy-Widom distribution governs height fluctuations in growth processes and is now shown to apply to nonequilibrium systems. A Fermi-Pasta-Ulam chain exhibits time-integrated current fluctuations following this distribution.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Physics
- Dynamical Systems
Background:
- The Tracy-Widom distribution, initially found in Gaussian unitary ensembles, is recognized for its role in height fluctuations of growth processes.
- Its potential applicability to other non-equilibrium systems remains an area of interest.
Purpose of the Study:
- To investigate the role of the Tracy-Widom distribution in one-dimensional systems with domain wall initial conditions.
- To explore the statistical properties of time-integrated currents in anharmonic chains under specific conditions.
Main Methods:
- Studying one-dimensional systems with domain wall initial conditions.
- Analyzing the behavior of a Fermi-Pasta-Ulam type anharmonic chain.
- Characterizing the time-integrated current and its fluctuations.
Main Results:
- The system develops a rarefaction wave, maintaining equilibrium states at the boundaries.
- The time-integrated current shows a deterministic component linear in time.
- Fluctuations in the current scale as t^(1/3) and follow a Tracy-Widom distribution.
Conclusions:
- The Tracy-Widom distribution is relevant for fluctuations in specific one-dimensional non-equilibrium systems.
- Anharmonic chains with domain wall initial conditions provide a physical realization of Tracy-Widom statistics in current fluctuations.
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