Liquid helium and the properties of a Bose–Einstein gas. III. The density dependence of hard-core models

1970 ◽  
Vol 48 (11) ◽  
pp. 1340-1364
Author(s):  
D. F. Goble
Keyword(s):  
Density Dependence ◽  
Liquid Helium ◽  
Hard Core ◽  
Ladder Approximation ◽  
Model Systems ◽  
Coordinate Space ◽  
Core Boundary ◽  
T Matrix ◽  
Bose Einstein ◽  
Space Method

We have used the results of a previous paper by Goble and Trainor to compute the density dependence of the hard-core Bose–Einstein gas in the t-matrix ladder approximation, utilizing the coordinate-space method of Brueckner and Sawada as modified by Parry and ter Haar, and the pseudopotential treatment of the hard-core boundary condition presented by Liu and Wong. Various thermodynamic parameters of these model systems are compared with the properties of liquid helium four. The disagreements which are found are shown to be primarily related to differences in the magnitudes of the Landau parameters.

Liquid helium and the properties of a Bose–Einstein gas. I. A numerical study of hard-core models

1968 ◽  
Vol 46 (7) ◽  
pp. 839-854 ◽  
Author(s):  
D. F. Goble ◽  
L. E. H. Trainor
Keyword(s):  
Liquid Helium ◽  
Numerical Study ◽  
Hard Core ◽  
Ladder Approximation ◽  
Pseudopotential Method ◽  
Coordinate Space ◽  
Core Potential ◽  
Soft Core Potential ◽  
Reasonable Choice ◽  
Bose Einstein

The properties of a hard-sphere, Bose–Einstein gas are investigated numerically in the t-matrix, ladder approximation, using both the coordinate-space treatment of Brueckner and Sawada, as modified by Parry and ter Haar, and the pseudopotential method of Liu and Wong. For each treatment, the form of the excitation spectrum and the thermodynamic properties of the gas at low temperatures are compared with the corresponding properties of liquid helium. The pseudopotential method gives better agreement for a reasonable choice of the radius of the "hard-core" interaction. This result is not surprising since the actual potential corresponding to the pseudopotential of Liu and Wong is intermediate between the "soft-core" potential of Brueckner and Sawada and a true "hard-core" potential.

Liquid Helium and the Properties of a Bose–Einstein Gas. IV. The Effect of Various Approximations

1971 ◽  
Vol 49 (24) ◽  
pp. 3099-3114 ◽  
Author(s):  
D. F. Goble
Keyword(s):  
Liquid Helium ◽  
Hard Core ◽  
Quantitative Agreement ◽  
Perturbation Series ◽  
Model System ◽  
Three Body ◽  
Bose Einstein ◽  
Generalized Condensation

On a qualitative basis we have examined the identification of the properties of a hard-core Bose–Einstein (BE) gas with those of liquid helium four below the lambda temperature. It is suggested that the use of the generalized condensation of Girardeau together with the inclusion of "three-body ladders" from the perturbation series may improve the agreement between the hard-core BE model system and the physical helium four system to such an extent that reasonable quantitative agreement may be attained.

Effects of the T-matrix center-of-mass approximation in the Brueckner–Sawada theory of liquid helium II

1985 ◽  
Vol 63 (12) ◽  
pp. 1548-1554
Author(s):  
S. K. Bose ◽  
D. F. Goble
Keyword(s):  
Liquid Helium ◽  
Center Of Mass ◽  
Interacting Particles ◽  
Excitation Spectra ◽  
Helium Ii ◽  
Mass Approximation ◽  
Interparticle Separation ◽  
T Matrix ◽  
The Difference ◽  
Bose Einstein

As a model for liquid helium II, we study the Bose–Einstein gas with a two-body interaction potential of the form ~δ(r − a), where r is the interparticle separation. Excitation spectra for various values of a are calculated using the Brueckner–Sawada approach based on the concept of the T matrix. However, unlike the work of Brueckner and Sawada and many other related works that followed, we take into account the dependence of the T matrix on the center-of-mass momentum of the interacting particles. Excitation spectra calculated with and without this dependence, using two different expressions for the two-particle propagator, indicate the validity of the Brueckner and Sawada center-of-mass approximation for physically interesting values of a. The difference between the two spectra is found to increase as a increases.

Systems with Condensates and Pairing

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Critical Parameters ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Pair Breaking ◽  
Systematic Theory ◽  
Bose Einstein Condensation ◽  
T Matrix ◽  
The Stability ◽  
Bose Einstein

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

GENERALIZED COOPER PAIRING IN SUPERCONDUCTORS

2007 ◽  
Vol 21 (21) ◽  
pp. 3657-3686 ◽  
Author(s):  
M. DE LLANO ◽  
J. F. ANNETT
Keyword(s):  
Center Of Mass ◽  
Power Series Expansion ◽  
Hard Core ◽  
Ladder Approximation ◽  
Common Element ◽  
Electron Interaction ◽  
Einstein Condensation ◽  
Cooper Pairing ◽  
Linear Dispersion ◽  
Energy Instability

We review Cooper pairing starting from its simplest, original 1956 version of two electrons interacting above the Fermi sea of an ideal Fermi gas (IFG). The two-electron interaction assumed extensively (if not exclusively), is the attractive two-parameter Cooper, and then BCS, model interactions. Hole Cooper pairs (CPs) and electron-hole CPs are then included along with the initial electron-CPs in terms of the single-fermion Green functions implied by the Bethe-Salpeter (BS) integral equation in the ladder approximation. A purely-imaginary CP energy "instability" is recovered that is well-documented in the literature at least since the late 1950's. A novel interpretation of this instability is that an unperturbed Hamiltonian different from the IFG one first used by Cooper suffices to obtain meaningful CPs. Instead of the IFG sea, a BCS-correlated Fermi "sea" used in the BS equation interpreted as the associated unperturbed Hamiltonian leads to real CP energies (with small imaginary terms implying damping). We survey how this has been achieved in 1D, 2D and 3D, and give a more detailed treatment in 2D. A vital distinction is that the original and generalized CPs are true bosons in contrast with BCS pairs that are not ordinary bosons but rather "hard-core bosons" as they do not obey strict Bose commutation rules. Another important common element of the original or generalized CPs (particularly in 2D where ordinary Bose-Einstein condensation (BEC) does not occur) is their linear dispersion relation in leading order in the total (or, center-of-mass) momentum power-series expansion of the CP energy. This theory encompasses, in principle, all empirically known superconductors including quasi-2D superconductors such as cuprates and the ET organic compounds, as well as quasi-1D ones such as the organometallic Bechgaard salts and nanotubes.

A coordinate-space study of kowalski's three-term separable approximation for the fully off-shell two-nucleon T-matrix

1975 ◽  
Vol 241 (3) ◽  
pp. 443-459 ◽  
Author(s):  
H.S. Picker ◽  
G.J. Stephenson
Keyword(s):  
Coordinate Space ◽  
Separable Approximation ◽  
T Matrix

The λ-Phenomenon of Liquid Helium and the Bose-Einstein Degeneracy

Nature ◽  
1938 ◽  
Vol 141 (3571) ◽  
pp. 643-644 ◽  
Author(s):  
F. LONDON
Keyword(s):  
Liquid Helium ◽  
Bose Einstein

A new model for the density-dependence of positive ion mobility in liquid helium

2011 ◽  
Author(s):  
F. Aitken ◽  
N. Bonifaci ◽  
A. Denat ◽  
K. von Haeften
Keyword(s):  
Density Dependence ◽  
Liquid Helium ◽  
Ion Mobility ◽  
New Model ◽  
Positive Ion
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