Harmonically confined Bose–Einstein condensation on the surface of a cylinder

2021 ◽  
pp. 2150285
Author(s):  
Meng-Jun Ou ◽  
Ji-Xuan Hou
Keyword(s):  
Einstein Condensation ◽  
Condensate Fraction ◽  
Two Dimensional ◽  
Canonical Partition Function ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Grand Canonical Partition Function ◽  
2D System ◽  
Bose Einstein ◽  
Grand Canonical

It is well known that Bose–Einstein condensation cannot occur in a free two-dimensional (2D) system. Recently, several studies have showed that BEC can occur on the surface of a sphere. We investigate BEC on the surface of cylinder on both sides of which atoms are confined in a one-dimensional (1D) harmonic potential. In this work, only the non-interacting Bose gas is considered. We determine the critical temperature and the condensate fraction in the geometry using the semi-classical approximation. Moreover, the thermodynamic properties of ideal bosons are also studied using the grand canonical partition function.

STUDY OF A NON-INTERACTING BOSON GAS

2002 ◽  
Vol 16 (03) ◽  
pp. 497-509 ◽  
Author(s):  
M. CORGINI ◽  
D. P. SANKOVICH
Keyword(s):  
Chemical Potential ◽  
Energy Operator ◽  
Upper Bounds ◽  
Model System ◽  
Einstein Condensation ◽  
Bose System ◽  
Canonical Partition Function ◽  
Grand Canonical Partition Function ◽  
Bose Einstein ◽  
Grand Canonical

For a non-interacting many particle Bose system whose energy operator is diagonal in the number of occupation operators [Formula: see text] upper bounds on the thermal averages [Formula: see text] are obtained. These bounds lead to the proof of Bose–Einstein condensation for finite values of the inverse temperature β and for chemical potential μ=0. Finally for μ<0, in the case of a generalization of the studied model system, the property of Local Gaussian Domination for the grand canonical partition function is proved.

scholarly journals Bose–Einstein condensation in one-dimensional optical lattices: Bogoliubov’s approximation and beyond

2016 ◽  
Vol 94 (7) ◽  
pp. 697-703
Author(s):  
Mohamed K. Al-Sugheir ◽  
Mufeed A. Awawdeh ◽  
Humam B. Ghassib ◽  
Emad Alhami
Keyword(s):  
Lattice Points ◽  
Effect Of Temperature ◽  
Einstein Condensation ◽  
Condensate Fraction ◽  
Number Density ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Different Temperatures ◽  
Bose Einstein

Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.

On Bose-Einstein Condensation

1954 ◽  
Vol 50 (1) ◽  
pp. 65-76 ◽  
Author(s):  
P. T. Landsberg
Keyword(s):  
Closed System ◽  
Canonical Ensemble ◽  
Energy Levels ◽  
Volume Density ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Quantum Numbers ◽  
Finite Integer ◽  
Bose Einstein ◽  
Grand Canonical

ABSTRACTThis paper contains a proof that the description of the phenomenon of Bose-Einstein condensation is the same whether (1) an open system is contemplated and treated on the basis of the grand canonical ensemble, or (2) a closed system is contemplated and treated on the basis of the canonical ensemble without recourse to the method of steepest descents, or (3) a closed system is contemplated and treated on the basis of the canonical ensemble using the method of steepest descents. Contrary to what is usually believed, it is shown that the crucial factor governing the incidence of the condensation phenomenon of a system (open or closed) having an infinity of energy levels is the density of states N(E) ∝ En for high quantum numbers, a condition for condensation being n > 0. These results are obtained on the basis of the following assumptions: (i) For large volumes V (a) all energy levels behave like V−θ, and (b) there exists a finite integer M such that it is justifiable to put for the jth energy level Ej= c V−θand to use the continuous spectrum approximation, whenever j ≥ M c θ τ are positive constants, (ii) All results are evaluated in the limit in which the volume of the gas is allowed to tend to infinity, keeping the volume density of particles a finite and non-zero constant. The present paper also serves to coordinate much of previously published work, and corrects a current misconception regarding the method of steepest descents.

On Bose-Einstein condensation in one-dimensional lattices of delta functions

2020 ◽  
Vol 35 (03) ◽  
pp. 2040005 ◽  
Author(s):  
M. Bordag
Keyword(s):  
Dimensional Case ◽  
Einstein Condensation ◽  
Periodic Lattice ◽  
Spectral Functions ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Free Case ◽  
Delta Functions ◽  
The One ◽  
Bose Einstein

We investigate Bose-Einstein condensation of a gas of non-interacting Bose particles moving in the background of a periodic lattice of delta functions. In the one-dimensional case, where one has no condensation in the free case, we showed that this property persist also in the presence of the lattice. In addition we formulated some conditions on the spectral functions which would allow for condensation.

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