CMT Forum: Tomohiro Sasomoto

01 Nov 2023
Seminars and colloquia
Time
Venue
Simpkins Lee
Speaker(s)

Prof. Tomohiro Sasomoto, Chiba University

Seminar series
CMT Forum
Knowledge of physics?
Yes, knowledge of physics required
For more information contact

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 [1]. 

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[2]. 

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] K. Mallick, H. Moriya, T. Sasamoto, Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process, PRL 129, 040601 (2022).