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.

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.

EFFECT OF HIGHER ORDER ENERGY CORRECTIONS INCLUDING THREE-BODY INTERACTION ON THE BOSE-EINSTEIN CONDENSATE WITH THE VARIATION OF REPULSIVE SELF INTERACTION ENERGY

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1690-1698 ◽  
Author(s):  
SHRI PRAKASH TEWARI ◽  
POONAM SILOTIA ◽  
ADITYA SAXENA ◽  
LOKESH KUMAR GUPTA
Keyword(s):  
Interaction Energy ◽  
Chemical Potential ◽  
Hard Core ◽  
Higher Order ◽  
Einstein Condensate ◽  
Body Interaction ◽  
Interaction Terms ◽  
Bose Einstein Condensate ◽  
Three Body ◽  
Bose Einstein

Various ground state properties such as chemical potential, differential and total energy per particle etc. of Bose-Einstein condensate of 10000 85 Rb atoms with varying repulsive self-interaction energy have been reported considering not only two-body interaction but also including the higher order terms of the low-density energy expansion of homogeneous Bose gas in the Ginzburg, Pitaevskii and Gross (GPG) equation. These include hard-core approximation of the bosons neglected earlier and the three-body interaction terms. The study is more general as it includes the terms beyond logarithm in energy density expansion. It is also shown that such a consideration does not violate the lower bound predicted earlier in which the 'constant' beyond logarithm term in the three-body interaction was neglected.

Effects of three-body interactions in the parametric and modulational instabilities of Bose–Einstein condensates

2011 ◽  
Vol 375 (48) ◽  
pp. 4288-4295 ◽  
Author(s):  
Etienne Wamba ◽  
Alidou Mohamadou ◽  
Thierry B. Ekogo ◽  
Jacque Atangana ◽  
Timoleon C. Kofane
Keyword(s):  
Modulational Instabilities ◽  
Three Body ◽  
Bose Einstein

scholarly journals Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Hiroyuki Tajima ◽  
Junichi Takahashi ◽  
Simeon Mistakidis ◽  
Eiji Nakano ◽  
Kei Iida
Keyword(s):  
Spectral Function ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Quantum Gas ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
Three Body ◽  
Bose Einstein ◽  
The Impact

The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose—Einstein Condensates with Two- and Three-Body Interactions

2014 ◽  
Vol 61 (2) ◽  
pp. 207-213
Author(s):  
Hai-Qin Jin ◽  
Jun-Rong He ◽  
Jian-Chu Liang ◽  
Ze-Bin Cai ◽  
Lin Yi
Keyword(s):  
Three Dimensional ◽  
Matter Wave ◽  
Wave Solutions ◽  
Three Body ◽  
Bose Einstein

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 Gastruloids develop the three body axes in the absence of extraembryonic tissues and spatially localised signalling

2017 ◽  
Author(s):  
D.A. Turner ◽  
L. Alonso-Crisostomo ◽  
M. Girgin ◽  
P. Baillie-Johnson ◽  
C. R. Glodowski ◽  
...  
Keyword(s):  
Embryonic Stem ◽  
Model System ◽  
The Body ◽  
Genetic Studies ◽  
Animal Development ◽  
Embryonic Tissues ◽  
Bmp Signalling ◽  
Three Body ◽  
Extraembryonic Tissues

AbstractEstablishment of the three body axes is a critical step during animal development. In mammals, genetic studies have shown that a combination of precisely deployed signals from extraembryonic tissues position the anteroposterior axis (AP) within the embryo and lead to the emergence of the dorsoventral (DV) and left-right (LR) axes. We have used Gastruloids, embryonic organoids, as a model system to understand this process and find that they are able to develop AP, DV and LR axes as well as to undergo axial elongation in a manner that mirror embryos. The Gastruloids can be grown for 160 hours and form derivatives from ectoderm, mesoderm and endoderm. We focus on the AP axis and show that in the Gastruloids this axis is registered in the expression of T/Bra at one pole that corresponds to the tip of the elongation. We find that localisation of T/Bra expression depends on the combined activities of Wnt/β-Catenin and Nodal/Smad2,3 signalling, and that BMP signalling is dispensable for this process. Furthermore, AP axis specification occurs in the absence of both extraembryonic tissues and of localised sources of signalling. Our experiments show that Nodal, together with Wnt/β-Catenin signalling, is essential for the expression of T/Bra but that Wnt signalling has a separable activity in the elongation of the axis. The results lead us to suggest that, in the embryo, the role of the extraembryonic tissues might not be to induce the axes but to bias an intrinsic ability of the embryo to break its initial symmetry and organise its axes.One sentence summaryCulture of aggregates of defined number of Embryonic Stem cells leads to self-organised embryo-like structures which, in the absence of localised signalling from extra embryonic tissues and under the autonomous influence of Wnt and Nodal signalling, develop the three main axes of the body.

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

Pramana ◽  
2009 ◽  
Vol 72 (2) ◽  
pp. 445-450
Author(s):  
Sk. Golam Ali ◽  
B. Talukdar ◽  
Aparna Saha
Keyword(s):  
Optical Lattice ◽  
Einstein Condensate ◽  
Atomic Interaction ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Three Body ◽  
Bose Einstein

scholarly journals Expansion dynamics in a one-dimensional hard-core boson model with three-body interactions

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Jie Ren ◽  
Yin-Zhong Wu ◽  
Xue-Fen Xu
Keyword(s):  
Hard Core ◽  
One Dimensional ◽  
Boson Model ◽  
Three Body
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