Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities – Yan Fyodorov (King’s College London)

When:
December 11, 2018 @ 11:30 am – 12:30 pm
2018-12-11T11:30:00+00:00
2018-12-11T12:30:00+00:00
Where:
Seminar Room 1
Newton Institute
Contact:

We study one-dimensional decaying Burgers turbulence with the covariance of initial profile of Gaussian-distributed velocities decaying as inverse square of the distance. Combining the heuristic replica trick of statistical mechanics with insights from the random matrix theory we reveal a freezing phase transition with decreasing viscosity. In the low-viscosity phase the one-point probability density of velocities becomes non-Gaussian reflecting a spontaneous one step replica symmetry breaking in the associated statistical mechanics problem. We obtain the low orders velocity cumulants analytically which favourably agree with numerical simulation. The presentation will be based on a joint work with P. Le Doussal and A. Rosso.