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Universal cumulants of the current in diffusive systems on a ring
C Appert-Rolland1, B Derrida, V Lecomte
1Laboratoire de Physique Théorique (CNRS UMR 8627), Université Paris-Sud 11, Bâtiment 210, 91405 Orsay cedex, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
We calculated key properties of the symmetric simple exclusion process. For large systems, both current and activity exhibit a universal scaling form, simplifying complex system analysis.
Area of Science:
- Statistical Mechanics
- Many-Body Physics
- Non-equilibrium Systems
Background:
- The symmetric simple exclusion process (SSEP) is a fundamental model in statistical mechanics.
- Understanding large deviation properties is crucial for characterizing complex systems.
- Previous studies have explored SSEP on various lattices, but universal scaling in both current and activity remained an open question.
Purpose of the Study:
- To exactly calculate the first cumulants of integrated current and activity in the SSEP on a ring.
- To investigate the large deviation functions for these quantities in the large system size limit.
- To identify and characterize any universal scaling behavior.
Main Methods:
- Exact calculation of cumulants using analytical methods.
- Analysis of Bethe ansatz equations for the SSEP.
- Application of fluctuating hydrodynamics and macroscopic fluctuation theory.
Main Results:
- The first cumulants of the integrated current and activity were precisely determined.
- For large system sizes, the large deviation functions of both current and activity were found to follow a universal scaling form.
- A single, identical scaling function describes both quantities.
Conclusions:
- The study reveals a surprising universality in the large deviation behavior of the symmetric simple exclusion process.
- The identified scaling function provides a unifying framework for understanding current and activity fluctuations.
- This universality can be explained through advanced theoretical frameworks like fluctuating hydrodynamics and macroscopic fluctuation theory.
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