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Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

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SRQW03 - Scaling limits & SPDEs: recent developments and future directions

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

This talk is part of the Isaac Newton Institute Seminar Series series.

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