Симметрийный подход в задаче о расширении газов в вакуум

Журнал экспериментальной и теоретической физики. 2021. Т. 159. № 4. С. 794–805.

Кузнецов Е. А., Kagan M.

A brief review of the results on the expansion of quantum and classical gases into a vacuum based on the use of symmetries is presented. For quantum gases in the Gross – Pitaevsky approximation, additional symmetries arise for gases with a chemical potential µ that depends on the density n in a power-law manner with exponent v = 2/D, where D is the dimension of space. For gas condensates of Bose atoms at temperatures T > 0, this symmetry occurs for two-dimensional systems. At D = 3 and, respectively, v = 2/3, this situation is realized for an interacting Fermi gas at low temperatures in the so-called unitary limit. The same symmetry for classical gases in three-dimensional geometry arises for gases with the adiabatic exponent gamma = 5/3. Both of these facts were discovered independently in 1970 by Talanov for the two-dimensional nonlinear Schrodinger (coinciding with the Gross – Pitaevsky equation), which describes the stationary self — focusing of light in media with Kerr nonlinearity, and for classical gases-by Anismov and Lysikov. In the quasi – classical limit, the Gross-Pitaevsky equations coincide with the equations of hydrodynamics of an ideal gas with the adiabatic exponent gamma = 1+2/D. Self-similar solutions in this approximation describe the angular deformations of a gas cloud against the background of an expanding gas in the framework of Ermakov-type equations. Such changes in the shape of an expanding cloud are observed in numerous experiments both during the expansion of a gas after exposure to high-power laser radiation, for example, on a metal, and during the expansion of quantum gases into a vacuum.

Keywords: virial theorem, теорема вириала, superfluid hydrodynamics, сверхтекучая гидродинамика, self-similar solution, Gross-Pitaevsky and Ermakov equations, unitary limit, уравнения Гросса-Питаевского и Ермакова, унитарный предел, cloud shape oscillations, expansion problem, осцилляции формы облака, автомодельное решение, задача разлёта

Publication based on the results of: Theoretical and experimental studies of promising heterogeneous structures for polymer photocells to increase their efficiency (2021)