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SUMMARY:Tomohiro Sasamoto (Tokyo Institute of Technology)
DTSTART:20220719T140000Z
DTEND:20220719T150000Z
DTSTAMP:20260801T122931Z
UID:IAMP_seminars/112
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IAMP_seminar
 s/112/">Mapping macroscopic fluctuation theory for the symmetric simple ex
 clusion process to a classically integrable system</a>\nby Tomohiro Sasamo
 to (Tokyo Institute of Technology) as part of One world IAMP mathematical 
 physics seminar\n\n\nAbstract\nThe large deviation principle for symmetric
  simple exclusion process(SEP) had been established by \nKipnis\, Olla\, V
 aradhan in 1989 [1]. A somewhat different formulation\, known as the macro
 scopic \nfluctuation theory (MFT)\, was initiated and developed by Jona-La
 sinio et al in 2000’s [2]. The basic \nequations of the theory\, MFT equ
 ations\, are coupled nonlinear partial differential equations and \nhave r
 esisted exact analysis except for stationary situation. In this talk we in
 troduce a novel \ngeneralization of the Cole-Hopf transformation and show 
 that it maps the MFT equations for SEP \nto the classically integrable Abl
 owitz-Kaup-Newell-Segur(AKNS) system. This allows us to solve \nthe equati
 ons exactly in time dependent regime by adapting standard ideas of inverse
  scattering method. \n\nThe talk is based on a joint work with Kirone Mall
 ick and Hiroki Moriya [3]. \n\nReferences\n\n[1] C. Kipnis\, S. Olla\, S. 
 R. S. Varadhan\, \nHydrodynamics and large deviations for simple exclusion
  processes\, Comm. Pure Appl. Math.\, 42:115–137\, 1989.\n\n[2] L. Berti
 ni\, A. De Sole\, D. Gabrielli\, G. Jona-Lasinio\, and C. Landim\,\nMacros
 copic fluctuation theory\, Rev. Mod. Phys.\, 87:593–636\, 2015.\n\n[3] K
 irone Mallick\, Hiroki Moriya\, Tomohiro Sasamoto\,\nExact solution of the
  macroscopic fluctuation theory for the symmetric exclusion process\,\narX
 iv: 2202.05213\, to appear in Phys. Rev. Lett.\n
LOCATION:https://researchseminars.org/talk/IAMP_seminars/112/
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