Symmetry Approach in the Problem of Gas Expansion into Vacuum
Abstract
A brief review of the results on the expansion of quantum and classical gases into vacuum based on the use of symmetries is presented. For quantum gases in the Gross–Pitaevskii (GP) approximation, additional symmetries arise for gases with a chemical potential μ that depends on the density n powerfully with exponent ν = 2/D, where D is the space dimension. For gas condensates of Bose atoms at temperatures T → 0, this symmetry arises for twodimensional systems. For D = 3 and, accordingly, ν = 2/3, this situation is realized for an interacting Fermi gas at low temperatures in the socalled unitary limit (see, for example, L. P. Pitaevskii, Phys. Usp. 51, 603 (2008)). The same symmetry for classical gases in threedimensional geometry arises for gases with the adiabatic exponent γ = 5/3. Both of these facts were discovered in 1970 independently by Talanov [V. I. Talanov, JETP Lett. 11, 199 (1970).] for a twodimensional nonlinear Schrödinger (NLS equation, which coincides with the Gross–Pitaevskii equation), describing stationary selffocusing of light in media with Kerr nonlinearity, and for classical gases, by Anisimov and Lysikov [S. I. Anisimov and Yu. I. Lysikov, J. Appl. Math. Mech. 34, 882 (1970)]. In the quasiclassical limit, these GP equations coincide with the equations of the hydrodynamics of an ideal gas with the adiabatic exponent γ = 1 + 2/D. Selfsimilar solutions in this approximation describe the angular deformations of the gas cloud against the background of an expanding gas by means of Ermakovtype equations. Such changes in the shape of an expanding cloud are observed in numerous experiments both during the expansion of gas after exposure to powerful laser radiation, for example, on metal, and during the expansion of quantum gases into vacuum.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 April 2021
 DOI:
 10.1134/S1063776121040130
 Bibcode:
 2021JETP..132..704K