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Abstract: We reveal a phase transition with decreasing viscosity $ u$ at u= u c>0in one-dimensional decaying Burgers turbulence with a power-law correlatedrandom profile of Gaussian-distributed initial velocities\sim|x-x-|^{-2}. The low-viscosity phase exhibits non-Gaussianone-point probability density of velocities, continuously dependent on u,reflecting a spontaneous one step replica symmetry breaking RSB in theassociated statistical mechanics problem. We obtain the low orders cumulantsanalytically. Our results, which are checked numerically, are based oncombining insights in the mechanism of the freezing transition in randomlogarithmic potentials with an extension of duality relations discoveredrecently in Random Matrix Theory. They are essentially non mean-field in natureas also demonstrated by the shock size distribution computed numerically anddifferent from the short range correlated Kida model, itself well described bya mean field one step RSB ansatz. We also provide some insights for the finiteviscosity behaviour of velocities in the latter model.



Author: Yan V Fyodorov, Pierre Le Doussal, Alberto Rosso

Source: https://arxiv.org/







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