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Current fluctuations in the Dyson gas.

Rahul Dandekar1, P L Krapivsky2,3, Kirone Mallick1

  • 1Commissariat à l'Energie Atomique Paris-Saclay, Institut de Physique Théorique, F-91191 Gif-sur-Yvette Cedex, France.

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Summary
This summary is machine-generated.

We analyzed current fluctuations in a Dyson gas using macroscopic fluctuation theory. This approach allows calculation of statistical properties for this complex one-dimensional system.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Non-equilibrium systems

Background:

  • Dyson gas models describe interacting particles in one dimension.
  • Macroscopic fluctuation theory (MFT) is a framework for studying current fluctuations.
  • Understanding large deviations in driven systems is crucial.

Purpose of the Study:

  • To adapt MFT for analyzing current fluctuations in a Dyson gas.
  • To derive and solve the governing equations for density and momentum evolution.
  • To compute the statistical properties of the current in this system.

Main Methods:

  • Adaptation of macroscopic fluctuation theory to the Dyson gas model.
  • Derivation of coupled nonlinear, nonlocal partial differential equations for density and momentum.
  • Solving a tractable boundary-value problem in an annealed setting with fluctuating initial conditions.

Main Results:

  • Successfully adapted MFT to the Dyson gas, yielding coupled PDEs.
  • Developed a method to handle mixed initial and final time boundary conditions.
  • Computed the cumulant generating function for the system's current.

Conclusions:

  • The study provides a theoretical framework for large fluctuation analysis in Dyson gases.
  • The derived equations and methods offer insights into non-equilibrium statistical mechanics.
  • This work enables the computation of detailed statistical properties of current in such systems.