Fluctuation effects in two-dimensional hydrodynamic systems
Effects due to interaction of long-wave fluctuations are studied. The distribution function for fluctuating quantities, making it possible to calculate their correlation functions, is derived. Due to an increasing number of variables, the distribution function is reduced to a form necessary for the construction of the Feynman diagram technique to calculate the correlation functions of the fluctuating quantities; properties of this diagram technique are considered. In the framework of this procedure it is shown that in two-dimensional hydrodynamic systems the fluctuation corrections to the dissipative term diverge logarithmically in the long-wave limit. The renormalization group equations, describing the long-wave behaviour of the dissipative terms, are derived; properties of this system of equations, associated with the fluctuation-dissipation theorem, are considered. Solutions of the renormalization group equations, revealing that the coefficient of \(k^ 2\) in the decrement of the gapless mode attenuation diverges as \((\ln (\Lambda /k))^{1/2}\), are found.
scientific article; zbMATH DE number 3968105