Институт теоретической физики им. Л.Д. Ландау РАН

L.D. Landau Institute for Theoretical Physics RAS

L.D. Landau Institute for Theoretical Physics RAS

"Quantum Fluids, Quantum Field Theory, and Gravity"

Expansion of the strongly interacting superfluid Fermi gas: symmetry and self-similar regimes

Date/Time: 15:10 20-Oct-2019

Abstract:

We consider an expansion of the strongly interacting superfluid Fermi gas in the vacuum in the so-called unitary regime when the chemical potential $\mu \propto \hbar^2n^{2/3}/m$ where $n$ is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. Such expansion can be described in the framework of the Gross-Pitaevskii equation (GPE) [1]. Because of the chemical potential dependence on the density $\sim n^{2/3}$ the GPE has additional symmetries resulting in existence of the virial theorem connected the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at $t\to\infty$ to the ballistic expansion of the gas. We carefully study such asymptotics and reveal a perfect matching between the quasi-classical self-similar solution and the ballistic expansion of the non-interacting gas [2]. This matching is governed by the virial theorem derived in [3] utilizing the Talanov transformation [4] which was first obtained for the stationary self-focusing of light in the media with cubic nonlinearity due to the Kerr effect. In the quasi-classical limit the equations of motion coincide with 3D hydrodynamics for the perfect gas with $\gamma=5/3$ which, as it was demonstrated by S.I. Anisimov and Yu.I. Lysikov [5], have additional symmetry. Just this symmetry provides one to find self-similar solution which describes,

on the background of the gas expansion, the angular deformations of the gas shape in the framework of the Ermakov-Ray-Reid type system.

The work of E.K. was performed under support of the Russian Science Foundation (grant 19-72-30028).

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{\bf References}

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\noindent [1] L.P. Pitaevskii, Superfluid Fermi liquid in a unitary

regime, Physics Uspekhi, v.51, pp.603-608, 2008.

\noindent [2] E.A. Kuznetsov, M.Yu. Kagan and

A.V. Turlapov. Expansion of the strongly interacting superfluid Fermi gas:

symmetries and self-similar regimes, arXiv:1903.04245 2019,

Phys. Rev. A (submitted).

\noindent [3] E.A. Kuznetsov, S.K. Turitsyn, Talanov

transformation in self-focusing problems and instability of stationary

waveguides, Phys.Lett., v.112 A, pp. 273-276, 1985.

\noindent [4] V.I. Talanov, On the self-focusing of light in the cubic

media, Pis'ma Zh.Eksp.Teor.Fiz., v.11, p.303, 1970.

\noindent [5] S.I. Anisimov and Yu.I. Lysikov. Expansion of a gas cloud in vacuum,

Journal of Applied Mathematics and Mechanics, v. 34, pp. 882--885,

1970.

on the background of the gas expansion, the angular deformations of the gas shape in the framework of the Ermakov-Ray-Reid type system.

The work of E.K. was performed under support of the Russian Science Foundation (grant 19-72-30028).

\vspace{0.2 cm}

{\bf References}

\vspace{0.2 cm}

\noindent [1] L.P. Pitaevskii, Superfluid Fermi liquid in a unitary

regime, Physics Uspekhi, v.51, pp.603-608, 2008.

\noindent [2] E.A. Kuznetsov, M.Yu. Kagan and

A.V. Turlapov. Expansion of the strongly interacting superfluid Fermi gas:

symmetries and self-similar regimes, arXiv:1903.04245 2019,

Phys. Rev. A (submitted).

\noindent [3] E.A. Kuznetsov, S.K. Turitsyn, Talanov

transformation in self-focusing problems and instability of stationary

waveguides, Phys.Lett., v.112 A, pp. 273-276, 1985.

\noindent [4] V.I. Talanov, On the self-focusing of light in the cubic

media, Pis'ma Zh.Eksp.Teor.Fiz., v.11, p.303, 1970.

\noindent [5] S.I. Anisimov and Yu.I. Lysikov. Expansion of a gas cloud in vacuum,

Journal of Applied Mathematics and Mechanics, v. 34, pp. 882--885,

1970.

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