scholarly journals Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

2011 ◽  
Vol 369 (1946) ◽  
pp. 2779-2799 ◽  
Author(s):  
Michael M. Scherer ◽  
Stefan Floerchinger ◽  
Holger Gies
Keyword(s):  
Scattering Length ◽  
Einstein Condensation ◽  
Many Body ◽  
Derivative Expansion ◽  
Functional Renormalization Group ◽  
Bose Einstein Condensation ◽  
Fermionic Atoms ◽  
Large Length ◽  
The Many ◽  
Bose Einstein

We review the functional renormalization group (RG) approach to the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation (BCS–BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

SUPERFLUID REGIMES IN DEGENERATE ATOMIC FERMI GASES

2006 ◽  
Vol 20 (19) ◽  
pp. 2739-2754
Author(s):  
G. V. SHLYAPNIKOV
Keyword(s):  
Scattering Length ◽  
Fermi Gases ◽  
Einstein Condensation ◽  
Weakly Bound ◽  
Future Studies ◽  
Bose Einstein Condensation ◽  
Ultracold Fermi Gases ◽  
Fermionic Atoms ◽  
Atom Interaction ◽  
Bose Einstein

We give a brief overview of recent studies of quantum degenerate regimes in ultracold Fermi gases. The attention is focused on the regime of Bose-Einstein condensation of weakly bound molecules of fermionic atoms, formed at a large positive scattering length for the interspecies atom-atom interaction. We analyze remarkable collisional stability of these molecules and draw prospects for future studies.

BOSE-EINSTEIN CONDENSATION OF ATOMS WITH ATTRACTIVE INTERACTION

1999 ◽  
Vol 13 (05n06) ◽  
pp. 625-631 ◽  
Author(s):  
N. AKHMEDIEV ◽  
M. P. DAS ◽  
A. V. VAGOV
Keyword(s):  
Statistical Physics ◽  
Scattering Length ◽  
Stationary Solutions ◽  
Attractive Potential ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Bose Einstein Condensation ◽  
Three Body ◽  
Negative Scattering Length ◽  
Bose Einstein

We suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.

scholarly journals Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

2017 ◽  
Vol 9 (5) ◽  
pp. 96
Author(s):  
M. Serhan
Keyword(s):  
Low Temperatures ◽  
Chemical Potential ◽  
Scattering Length ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Atomic Gases ◽  
Bose Einstein Condensation ◽  
Gaussian Type ◽  
Negative Scattering Length ◽  
Bose Einstein

In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.

scholarly journals Multi-regulator functional renormalization group for many-fermion systems

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740027
Author(s):  
Yuya Tanizaki ◽  
Tetsuo Hatsuda
Keyword(s):  
Renormalization Group ◽  
Collective Excitations ◽  
Einstein Condensation ◽  
Point Function ◽  
Functional Renormalization Group ◽  
Fermionic System ◽  
Bose Einstein Condensation ◽  
Fermion Systems ◽  
Two Component ◽  
Bose Einstein

We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.

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