Fluctuation effects in twodimensional hydrodynamic systems
Abstract
Effects due to interaction of longwave 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 twodimensional hydrodynamic systems the fluctuation corrections to the dissipative term diverge logarithmically in the longwave limit. The renormalization group equations, describing the longwave behaviour of the dissipative terms, are derived; properties of this system of equations, associated with the fluctuationdissipation 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(Λ/k)) ^{{1}/{2}}, are found.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 June 1984
 DOI:
 10.1016/03784371(84)90147X
 Bibcode:
 1984PhyA..126..135K