Theory of a Condensed Charged-Bose Charged Fermi Gas and Ginzburg-Landau Studies of Superfluid HELIUM-3.

We discuss a superfluid phase transition in a trapped neutral-atom Fermi gas. We consider the case where the critical temperature greatly exceeds the spacing between the trap levels and derive the corresponding Ginzburg-Landau equation. The latter turns out to be analogous to the equation for the condensate wave function in a trapped Bose gas. The analysis of its solution provides us with the value of the critical temperature ${T}_{c}$ and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.We discuss a superfluid phase transition in a trapped neutral-atom Fermi gas. We consider the case where the critical temperature greatly exceeds the spacing between the trap levels and derive the corresponding Ginzburg-Landau equation. The latter turns out to be analogous to the equation for the condensate wave function in a trapped Bose gas. The analysis of its solution provides us with the value of the critical temperature ${T}_{c}$ and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.

arXiv:cond-mat/9712262Physical Review AAug 1, 199858 citations

Theory of a superfluid Fermi liquid

Alexander I. Akhiezer, Красильников Владимир Владимирович, S.V. Peletminskii +1 more

Uspekhi Fizicheskih NaukJan 1, 199315 citations

Evolution from BCS to BEC Superfluidity in p -Wave Fermi Gases

M. Iskin, C. A. R. Sá de Melo

We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.

arXiv:cond-mat/0510300Physical Review LettersJan 31, 200677 citations

On the theory of a superfluid Fermi liquid

Красильников Владимир Владимирович, S.V. Peletminskij, A. A. Yatsenko

Physica A Statistical Mechanics and its ApplicationsJan 1, 199014 citations

Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

Filippo Pascucci, Andrea Perali, Luca Salasnich

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

arXiv:2204.03590Condensed MatterDec 1, 20212 citations

{T}_{c}

and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.