Tomohiro Sasamoto

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

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).