Exact solution for macroscopic fluctuation theory for 1D symmetric exclusion process

The macroscopic fluctuation theory (MFT), initiated and developed by Jona-Lasinio et al in 2000’s,  is a theory for studying large deviations of non-equilibrium many-body systems [1]. A basic model in the theory is the symmetric simple exclusion process(SEP), for which the large deviation principle had been established even earlier by Kipnis, Olla, Varadhan in 1989 [2]. 

The basic equations of the theory, MFT equations, are coupled nonlinear partial differential equations and have resisted exact analysis except for stationary and non-interacting situations. Last year we have found that a novel generalization of the Cole-Hopf transformation maps the MFT equations for 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 [3]. Related results for different models will be also discussed. 

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

References
[1] L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim,
Macroscopic fluctuation theory, Rev. Mod. Phys., 87:593–636, 2015.

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

[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. 

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