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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.