Fluctuation effects in two-dimensional hydrodynamic systems
type: Item
instance of: scholarly article
title: Fluctuation effects in two-dimensional hydrodynamic systems
zbMATH Open document ID: 0599.76008
DOI: 10.1016/0378-4371(84)90147-X
author: I. M. Khalatnikov
author: V. V. Lebedev
author: A. I. Sukhorukov
published in: Physica A
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 82D15
zbMATH DE Number: 3968105
zbMATH Keywords: long-wave fluctuations
zbMATH Keywords: distribution function
zbMATH Keywords: correlation functions
zbMATH Keywords: Feynman diagram technique
zbMATH Keywords: two-dimensional hydrodynamic systems
zbMATH Keywords: dissipative term
zbMATH Keywords: long-wave limit
zbMATH Keywords: renormalization group equations
zbMATH Keywords: fluctuation-dissipation theorem
zbMATH Keywords: gapless mode attenuation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3968105