Note on the Canonical Ensemble for the Ideal Einstein‐Bose Gas

1957 ◽  
Vol 27 (4) ◽  
pp. 931-932 ◽  
Author(s):  
J. Ford ◽  
T. H. Berlin
Keyword(s):  
Canonical Ensemble ◽  
Bose Gas ◽  
The Ideal

Condensation of the Ideal Bose Gas as a Cooperative Transition

1968 ◽  
Vol 166 (1) ◽  
pp. 152-158 ◽  
Author(s):  
J. D. Gunton ◽  
M. J. Buckingham
Keyword(s):  
Bose Gas ◽  
Cooperative Transition ◽  
Ideal Bose Gas ◽  
The Ideal

A comment on the ideal relativistic Bose gas

1981 ◽  
Vol 14 (11) ◽  
pp. 3013-3016 ◽  
Author(s):  
J Dunning-Davies
Keyword(s):  
Bose Gas ◽  
The Ideal

ON THE LOW-TEMPERATURE BEHAVIOR OF THE INFINITE-VOLUME IDEAL BOSE GAS

2010 ◽  
Vol 13 (01) ◽  
pp. 39-63
Author(s):  
KARL-HEINZ FICHTNER ◽  
KEI INOUE ◽  
MASANORI OHYA
Keyword(s):  
Low Temperature ◽  
Numerical Simulations ◽  
Bose Gas ◽  
Temperature Behavior ◽  
Infinite Volume ◽  
Position Distribution ◽  
Bounded Volume ◽  
Ideal Bose Gas ◽  
The Ideal

In Ref. 11 clustering representations of the position distribution of the ideal Bose gas were considered. In principle that gives rise to possibilities concerning simulations of the system of positions of the particles. But one has to take into account that in case of low temperature the clusters are very large and their origins are far from a fixed bounded volume. For that reason we will consider some estimations of the influence of these clusters on the behavior of the subsystem of particles located in a fixed bounded volume. All points in the fixed bounded volume come from a bigger volume which the estimation (5.2) in Theorem 5.2 gives on average. Several numerical simulations in dimension two are shown in Sec. 5.

THERMODYNAMICS OF A BOSE GAS TRAPPED IN A BOUNDED HARMONIC POTENTIAL

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5855-5873 ◽  
Author(s):  
SHALINI LUMB ◽  
S. K. MUTHU
Keyword(s):  
Critical Temperature ◽  
Constant Pressure ◽  
Coefficient Of Thermal Expansion ◽  
Local Equilibrium ◽  
Bose Gas ◽  
Harmonic Potential ◽  
Sharp Drop ◽  
Oscillator Length ◽  
Good Agreement ◽  
The Ideal

Some thermodynamic features of an assembly of a finite number of bosons trapped in a bounded harmonic potential are investigated. P–V isotherms are drawn for both the degenerate and the non-degenerate phases. At any temperature, the pressure is a decreasing function of volume, unlike the free Bose gas for which the pressure becomes independent of volume in the degenerate phase. At the absolute zero of temperature the quantum pressure for a spherical enclosure of radius r0 equal to aho, aho being the characteristic harmonic oscillator length, is found to be of order 10-10 Torr while for [Formula: see text] it is of order 10-12 Torr. The isothermal compressibility has a sharp drop near the critical point and becomes negligibly small for temperatures above the critical temperature, irrespective of the size of the trap. The coefficient of thermal expansion also shows a sudden drop at the critical temperature. The specific heat at constant pressure shows a peak and is well-defined in the degenerate phase, in contradistinction to the ideal Bose gas. Results recently derived by Singh on the basis of local equilibrium theory are found to be in good agreement with our numerical computations.

scholarly journals Condensation of ideal Bose gas confined in a box within a canonical ensemble

2007 ◽  
Vol 76 (6) ◽  
Author(s):  
Konstantin Glaum ◽  
Hagen Kleinert ◽  
Axel Pelster
Keyword(s):  
Canonical Ensemble ◽  
Bose Gas ◽  
Ideal Bose Gas

Order Parameter, Mean-Field Theory, and the Ideal Bose Gas

1969 ◽  
Vol 188 (1) ◽  
pp. 522-525 ◽  
Author(s):  
M. Schick ◽  
P. R. Zilsel
Keyword(s):  
Field Theory ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Bose Gas ◽  
Ideal Bose Gas ◽  
The Ideal

Excitations in a Bose gas at finite temperatures. I. Shielded potential in the Hartree approximation

1970 ◽  
Vol 48 (18) ◽  
pp. 2135-2154 ◽  
Author(s):  
T. H. Cheung ◽  
Allan Griffin
Keyword(s):  
Particle Interaction ◽  
Bose Gas ◽  
Theoretical Description ◽  
Convincing Evidence ◽  
Repulsive Interaction ◽  
Potential Approximation ◽  
First Order ◽  
Excited Atoms ◽  
Self Energy ◽  
The Ideal

Making use of the finite-temperature version of Beliaev's field-theoretical description of an interacting Bose gas, we sum the self-energy diagrams which correspond to the collisionless shielded potential approximation (SPA). This generalizes Bogoliubov's first-order results by replacing the bare repulsive interaction by a dynamically shielded interaction and includes the effect of the excited atoms. This theory is completely equivalent to that of Tserkovnikov if we use the ideal Bose gas approximation for the polarization function which screens the two-particle interaction. The excitation spectrum is found to have a single resonance. We do not find any convincing evidence for the additional high frequency second sound mode obtained by Tserkovnikov.

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