Unitarity Schrodinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover

On the basis of quantum hydrodynamical equations we derive a unitarity Schrodinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg-Laudau-type equation for the fermionic Cooper pairs in the BCS sid...

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Bibliographic Details
Published in:Chinese physics letters 2010-04, Vol.27 (4), p.21-24, Article 040304
Main Author: 张文渊 王成涛 马永利
Format: Article
Language:English
Subjects:
BCS
Crossovers
Fermi gases
Fluids
Ground state
Mathematical analysis
Schroedinger equation
Superfluidity
Wave functions
基态性质
流体动力学方程
统一性
薛定谔方程
费米气体
超流态
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Summary:On the basis of quantum hydrodynamical equations we derive a unitarity Schrodinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg-Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross-Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrodinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.
ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/27/4/040304