### Macroscopic fluctuation theory for the symmetric simple exclusion process and a classical integrable system

Mathematical Physics Seminar

24th November 2023, 1:45 pm – 3:30 pm

Fry Building, 2.04

The large deviation principle for symmetric simple exclusion process(SEP) had been established by

Kipnis, Olla, Varadhan in 1989 [1]. A somewhat different formulation, known as the macroscopic

fluctuation theory (MFT), was initiated and developed by Jona-Lasinio et al in 2000’s [2]. The basic

equations of the theory, MFT equations, are coupled nonlinear partial differential equations and

have resisted exact analysis except for stationary situation. In this talk we introduce a generalization

of the Cole-Hopf transformation and show that it maps the MFT equations for a few symmetric diffusive systems including SEP to the classically integrable Ablowitz-Kaup-Newell-Segur(AKNS) system. This allows us to solve the equations exactly in time dependent regime by adapting standard ideas of inverse scattering method.

The talk is based on a joint work with Kirone Mallick and Hiroki Moriya [3].

References

[1] C. Kipnis, S. Olla, S. R. S. Varadhan, Hydrodynamics and large deviations for simple exclusion processes, Comm. Pure Appl. Math., 42:115–137, 1989.

[2] L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim,

Macroscopic fluctuation theory, Rev. Mod. Phys., 87:593–636, 2015.

[3] Kirone Mallick, Hiroki Moriya, Tomohiro Sasamoto,

Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process,

Phys. Rev. Lett. 129, 040601 (2022) (arXiv: 2202.05213).

*Organiser*: Thomas Bothner

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