Prof. Tomohiro Sasomoto, Chiba University
Abhi Prakash, email@example.com
Exact solution for macroscopic fluctuation theory for 1D stochastic interacting particle systems
The macroscopic fluctuation theory (MFT), initiated and developed by Jona-Lasinio et al in 2000’s,
is a theory for studying large fluctuations of non-equilibrium many-body systems .
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.
In this talk we show that, for a class of stochastic interacting particle systems, a generalization of the Cole-Hopf transformation maps their MFT equations 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. A model of our primary interest is the symmetric simple exclusion process (SEP), which is considered to be one of the most fundamental models of non-equilibrium statistical mechanics, but our method can be applied simultaneously to other important models such as the Kipnis-Marccioro-Presutti(KMP) model of energy diffusion.
The talk is based on a collaborations with K. Mallick and H. Moriya.
 L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Macroscopic fluctuation theory, Rev. Mod. Phys., 87:593–636, 2015.
 K. Mallick, H. Moriya, T. Sasamoto, Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process, PRL 129, 040601 (2022).