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

2021 ◽  
Author(s):  
Filippo Pascucci ◽  
Andrea Perali ◽  
Luca Salasnich
Keyword(s):  
Landau Theory ◽  
Landau Equation ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Einstein Condensate ◽  
Unitary Limit ◽  
Ginzburg Landau ◽  
Gaussian Fluctuations ◽  
Physical Quantities ◽  
Different Levels

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.

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

2021 ◽  
Vol 6 (4) ◽  
pp. 49
Author(s):  
Filippo Pascucci ◽  
Andrea Perali ◽  
Luca Salasnich
Keyword(s):  
Landau Theory ◽  
Landau Equation ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Unitary Limit ◽  
Ginzburg Landau ◽  
Gaussian Fluctuations ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Physical Quantities

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.

Three-dimensional dissipative optical solitons

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Dumitru Mihalache
Keyword(s):  
Landau Equation ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Optical Solitons ◽  
Ginzburg Landau ◽  
Systematic Analysis ◽  
Dissipative Solitons ◽  
Existence Domain ◽  
Existence And Stability ◽  
The Stability

AbstractA brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane.

scholarly journals Bounded solutions for an ordinary differential system from the Ginzburg–Landau theory

2020 ◽  
Vol 150 (6) ◽  
pp. 3378-3408
Author(s):  
Anne Beaulieu
Keyword(s):  
Bounded Solution ◽  
Landau Theory ◽  
Landau Equation ◽  
The Other ◽  
Two Dimensional ◽  
Bounded Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Specific Contribution ◽  
Solution Problem

In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg–Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the Ginzburg–Landau equation by translations and rotations. The specific contribution of our work is to prove that in the other cases, the system does not admit any bounded solutions. We show that this bounded solution problem is related to an eigenvalue problem.

Quantum fluctuations in the time-dependent BCS–BEC crossover

2008 ◽  
Vol 366 (1877) ◽  
pp. 2813-2820 ◽  
Author(s):  
B.M Breid ◽  
J.R Anglin
Keyword(s):  
Landau Theory ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Integral Approach ◽  
Saddle Point Approximation ◽  
Ginzburg Landau ◽  
Bose Einstein Condensate ◽  
Fermionic Atoms ◽  
Molecular Fields ◽  
Bose Einstein

We describe the time-dependent formation of a molecular Bose–Einstein condensate from a BCS state of fermionic atoms as a result of slow sweeping through a Feshbach resonance. We apply a path integral approach for the molecules, and use two-body adiabatic approximations to solve the atomic evolution in the presence of the classical molecular fields, obtaining an effective action for the molecules. In the narrow resonance limit, the problem becomes semiclassical, and we discuss the growth of the molecular condensate in the saddle point approximation. Considering this time-dependent process as an analogue of the cosmological Zurek scenario, we compare the way condensate growth is driven in this rigorous theory with its phenomenological description via time-dependent Ginzburg–Landau theory.

scholarly journals Fluctuation conductivity in two-band superconductor SmFeAsO0.8F0.2

2015 ◽  
Vol 33 (3) ◽  
pp. 644-648 ◽  
Author(s):  
I.N. Askerzade ◽  
R. T. Tagiyeva Askerbeyli
Keyword(s):  
Magnetic Field ◽  
Landau Theory ◽  
Three Dimensional ◽  
Band Model ◽  
Ginzburg Landau ◽  
Band Theory ◽  
Fluctuation Conductivity ◽  
Temperature Dependences ◽  
Two Band Model ◽  
Good Agreement

Abstract In this study we have calculated the fluctuation conductivity near critical temperature of SmFeAsO0.8F0.2 superconductor using two-band Ginzburg-Landau theory. It was illustrated that in the absence of external magnetic field, the two-band model reduced to a single effective band theory with modified temperature dependences. The calculations revealed three-dimensional character of fluctuations of conductivity in the new Fe-based superconductor SmFeAsO0.8F0.2. It has been shown that such a model is in good agreement with experimental data for this compound.

Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation

2006 ◽  
Vol 97 (7) ◽  
Author(s):  
D. Mihalache ◽  
D. Mazilu ◽  
F. Lederer ◽  
Y. V. Kartashov ◽  
L.-C. Crasovan ◽  
...  
Keyword(s):  
Landau Equation ◽  
Three Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Stable Vortex
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