Speaker
Description
The large deviations for the diffusion of a tracer in a 1D time dependent medium can be described, on diffusive scales,
by the macroscopic fluctuation theory (MFT).
The corresponding MFT variational equations are mapped to the integrable derivative non-linear Schrodinger
equation. We provide a solution using inverse scattering methods, and obtain the large deviation rate function
for the sample to sample fluctuation of the probability of the tracer position.
Furthermore by varying the position of the tracer, i.e. the asymmetry, we uncover the
full integrable crossover from the MFT to the weak noise theory of the KPZ equation, matching
our previous results for the latter problem.
Based on
Krajenbrink, A., & Le Doussal, P. (2023). Crossover from the macroscopic fluctuation theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion. Physical Review E, 107(1), 014137.
