Self-consistentt-matrix theory of the Hartree-Fock-Bogoliubov approximation for Bose-Einstein-condensed systems

2012 ◽  
Vol 85 (3) ◽  
Author(s):  
Ha Kim ◽  
Cheng Song Kim ◽  
Chang Liol Huang ◽  
He-Shan Song ◽  
Xue-Xi Yi
Keyword(s):  
Matrix Theory ◽  
Hartree Fock ◽  
Bogoliubov Approximation ◽  
Bose Einstein ◽  
Condensed Systems

scholarly journals SIMULTANEOUS ONSET OF CONDENSATION OF MOLECULES AND ATOMS IN AN ATTRACTIVE FERMI GAS OF ATOMS

2007 ◽  
Vol 21 (01) ◽  
pp. 51-58
Author(s):  
FUXIANG HAN ◽  
MINGHAO LEI ◽  
E WU
Keyword(s):  
Critical Temperature ◽  
Fermi Gas ◽  
Order Parameters ◽  
Einstein Condensation ◽  
Grand Partition Function ◽  
Path Integral Representation ◽  
Hartree Fock ◽  
Bogoliubov Approximation ◽  
The Common ◽  
Bose Einstein

The self-consistent equations for the order parameters of Bose–Einstein condensation (BEC) of molecules and Bardeen–Cooper–Schrieffer (BCS) condensation of atoms in a Fermi gas of atoms with an attractive two-body interaction between atoms have been derived within the Hartree–Fock–Bogoliubov approximation from the path integral representation of the grand partition function. We have found that the order parameters for BEC and BCS are proportional to each other, which implies that BEC and BCS onsets simultaneously. We have also found that the common critical temperature of BEC and BCS increases as the average number of molecules increases and that the atom-molecule coupling enhances the common critical temperature.

VALIDITY OF THE BOGOLIUBOV APPROXIMATION FOR THE BOSE-EINSTEIN CONDENSATION IN A TRAP

2012 ◽  
Vol 17 ◽  
pp. 140-148 ◽  
Author(s):  
HIROSHI EZAWA ◽  
KEIJI WATANABE ◽  
KOICHI NAKAMURA
Keyword(s):  
Single Particle ◽  
The State ◽  
Trapping Potential ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Single Particle Level ◽  
Bogoliubov Approximation ◽  
Particle Level ◽  
Particle Potential ◽  
Bose Einstein

In treating system of bosons localized in a trapping potential, having a macroscopic number N0 of them condensing at the lowest single-particle level v0, Bogoliubov approximation is to replace the creation/annihilation operators [Formula: see text] of the state v0 by [Formula: see text]. We show that this approximation is justified if the inter-particle potential is repulsive in the sense specified. In fact, we show, by using [Formula: see text], that [Formula: see text] is effectively of the order [Formula: see text] under the condition stated.

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