Intermittency effects in Burgers equation

Intermittency effects in Burgers equation driven by thermal noise. Abstract For the Burgers equation driven by thermal noise leading asymp-totics of pair and high-order correlators of the velocity field are found for finite times and large distances. It is shown that the intermittency takes place: some correlators are much larger than their reducible parts. Intermittency implies strong non-Gaussianity of statistics of fluctuating fields. This phenomenon is shown by hydrodynamical systems in a state of developed turbulence[1, 2, 3]. In such far from equilibrium situations intermittency appears as prevalence of irreducible parts of some fourth order simultaneous correlators over reducible ones. As for thermal equilibrium, irreducible parts of simultaneous correlators of local fluctuating fields turn out to be of the same order as their Gaussian parts even in critical region. This property is inherent in the renormaliza-tion group method which takes care of interaction of fluctuations through renormalization of local field and effective Hamiltonian [4]. In the recent paper [5] V.V.Lebedev disclosed that the picture can change drastically when we pass to time-dependent correlations of thermally fluctuating quantities. He found that in the low-temperature phase of two-dimensional systems of the Berezinskii-Kosterlitz-Thouless kind different-time correlation functions of the vortex charge density may greately exeed their own Gaussian part. In the same paper [5] the physical cause of such 1