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Updated: Jun 15, 2026
07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Integrability and exact large deviations of the weakly asymmetric exclusion process
Alexandre Krajenbrink1, Pierre Le Doussal2
1Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom and Le Lab Quantique, 58 rue d'Hauteville, 75010 Paris, France.
Physical Review. E
|February 20, 2026
Summary
The weakly asymmetric exclusion process (WASEP) is described by macroscopic fluctuation theory (MFT). This study derives exact formulas for currents and tracer positions, revealing a crossover to Kardar-Parisi-Zhang (KPZ) equation dynamics.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Physics
- Complex Systems
Background:
- The weakly asymmetric exclusion process (WASEP) is a key model for interacting particles in one dimension.
- Macroscopic fluctuation theory (MFT) provides a framework for describing such systems under driving.
- Understanding crossovers between different dynamic regimes is crucial in non-equilibrium statistical mechanics.
Purpose of the Study:
- To derive exact formulas for statistical properties of the WASEP.
- To analyze the crossover from WASEP to Kardar-Parisi-Zhang (KPZ) equation dynamics.
- To investigate the integrability of the MFT for the WASEP.
Main Methods:
- Microscopic derivation of cumulant generating functions and large deviation rate functions.
- Analysis of scaling exponents for currents and tracer positions.
- Mapping the MFT to a complex extension of the anisotropic Landau-Lifshitz spin chain to demonstrate integrability.
Main Results:
- Exact formulas for the time-integrated current and tracer position in the WASEP.
- Characterization of the crossover from WASEP (cubic tail) to KPZ (5/2 and 3/2 tail) exponents with increasing asymmetry.
- Demonstration of the classical integrability of the MFT for the WASEP via Lax pairs.
Conclusions:
- The MFT of the WASEP accurately describes the crossover to KPZ dynamics.
- The WASEP MFT is classically integrable, extending to other asymmetric models.
- This work provides a unified framework for understanding driven particle systems.
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