Ground-State Energy of a Weakly Interacting Bose Gas: Calculation Without Regularization

2004 ◽  
Vol 59 (1-2) ◽  
pp. 1-13 ◽  
Author(s):  
Christoph Weiss ◽  
Martin Block ◽  
Dave Boers ◽  
André Eckardt ◽  
Martin Holthaus
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Born Approximation ◽  
State Energy ◽  
Low Density ◽  
Density Character ◽  
Dilute Gas ◽  
Bogoliubov Approximation ◽  
Soft Interaction ◽  
Additional Device

The textbook calculation of the ground-state energy of a dilute gas of Bose particles is examined in detail, and certain mathematical inconsistencies are pointed out. On the basis of this analysis, a refined approach suitable for soft interaction potentials which lend themselves to a low-order Born approximation is developed. This procedure emphasizes the low-density character of the resulting formula for the ground-state energy, and avoids all divergent expressions at intermediate stages of the computation. It is stressed that the standard Bogoliubov approximation, if not augmented by some additional device, leads to an error which manifests itself already in the lowest order of the density. - PACS 03.75.Hh, 05.30.Jp, 03.65.Nk.

scholarly journals Ground State Energy of the Low Density Hubbard Model

2008 ◽  
Vol 131 (6) ◽  
pp. 1139-1154 ◽  
Author(s):  
Robert Seiringer ◽  
Jun Yin
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Low Density

scholarly journals Ground-state energy of a low-density Bose gas: A second-order upper bound

2008 ◽  
Vol 78 (5) ◽  
Author(s):  
László Erdős ◽  
Benjamin Schlein ◽  
Horng-Tzer Yau
Keyword(s):  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Bose Gas ◽  
Second Order ◽  
Low Density

scholarly journals Ground State Energy of the Low Density Bose Gas

1998 ◽  
Vol 80 (12) ◽  
pp. 2504-2507 ◽  
Author(s):  
Elliott H. Lieb ◽  
Jakob Yngvason
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Bose Gas ◽  
Low Density

GROUND-STATE ENERGY OF THE ELECTRON GAS WITH THE MODIFIED COULOMB POTENTIAL 1/rp

2011 ◽  
Vol 25 (15) ◽  
pp. 2019-2030
Author(s):  
LIANGJIE FU ◽  
YUAN CHEN
Keyword(s):  
Ground State Energy ◽  
Coulomb Potential ◽  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Electron Gas ◽  
High Density ◽  
Low Density ◽  
Density Limit ◽  
Low Density Limit

In this paper, due to the effect of positively-charged screening holes, Coulomb potential energy 1/r is modified to be 1/rp, which is assumed to deviate slightly from the former. Using many-body perturbation theory, we obtain a simple analytic representation of the ground-state energy and correlation energy for a uniform electron gas. Our results agree with those obtained by the numerical and semi-analytic methods at low-density limit. Higher ground-state energies at high-density limit are calculated from our model. High order r expansion terms are found at high-density region. A curve of transition density versus p is drawn via the Misawa spin-scaling relation, which is in consistent with Perdew's study at low-density limit.

scholarly journals Ground-state energy of the low-density Fermi gas

2005 ◽  
Vol 71 (5) ◽  
Author(s):  
Elliott H. Lieb ◽  
Robert Seiringer ◽  
Jan Philip Solovej
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Fermi Gas ◽  
Low Density
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