TY - JOUR

T1 - Expansion of the strongly interacting superfluid Fermi gas

T2 - Symmetries and self-similar regimes

AU - Kuznetsov, E. A.

AU - Kagan, M. Yu

AU - Turlapov, A. V.

PY - 2020/4

Y1 - 2020/4

N2 - We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum in the so-called unitary regime when the chemical potential μ 2n2/3/m, where n is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. At low temperatures T→0, such an expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). For such a dependence of the chemical potential on the density, the GPE has additional symmetries, resulting in the existence of the virial theorem, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at t→∞ to the gas cloud expansion, linearly growing in time. We study such asymptotics and reveal the perfect match between the quasiclassical self-similar solution and the asymptotic expansion of the noninteracting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasiclassical limit, the equations of motion coincide with three-dimensional hydrodynamics for the perfect monatomic gas with γ=5/3. Their self-similar solution describes, within the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov-Ray-Reid-type system.

AB - We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum in the so-called unitary regime when the chemical potential μ 2n2/3/m, where n is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. At low temperatures T→0, such an expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). For such a dependence of the chemical potential on the density, the GPE has additional symmetries, resulting in the existence of the virial theorem, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at t→∞ to the gas cloud expansion, linearly growing in time. We study such asymptotics and reveal the perfect match between the quasiclassical self-similar solution and the asymptotic expansion of the noninteracting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasiclassical limit, the equations of motion coincide with three-dimensional hydrodynamics for the perfect monatomic gas with γ=5/3. Their self-similar solution describes, within the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov-Ray-Reid-type system.

UR - http://www.scopus.com/inward/record.url?scp=85084916750&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.101.043612

DO - 10.1103/PhysRevA.101.043612

M3 - Article

AN - SCOPUS:85084916750

VL - 101

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 043612

ER -