Bose—Einstein Condensation in a One-Dimensional Model with Random Impurities

1973 ◽  
Vol 7 (2) ◽  
pp. 712-720 ◽  
Author(s):  
J. M. Luttinger ◽  
H. K. Sy
Keyword(s):  
Einstein Condensation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Bose Einstein

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.

Thermodynamic Properties of a q-Boson Gas Trapped in an n-Dimensional Harmonic Potential

2003 ◽  
Vol 10 (02) ◽  
pp. 135-145 ◽  
Author(s):  
Guozhen Su ◽  
Lixuan Chen ◽  
Jincan Chen
Keyword(s):  
Heat Capacity ◽  
Distribution Function ◽  
Critical Temperature ◽  
Thermodynamic Properties ◽  
Harmonic Potential ◽  
Einstein Condensation ◽  
Dimensional System ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Bose Einstein

The thermodynamic properties of an ideal q-boson gas trapped in an n-dimensional harmonic potential are studied, based on the distribution function of q-bosons. The critical temperature Tc,q of Bose-Einstein condensation (BEC) and the heat capacity C of the system are derived analytically. It is shown that for the q-boson gas trapped in a harmonic potential, BEC may occur in any dimension when q ≠ 1, the critical temperature is always higher than that of an ordinary Bose gas (q = 1), and the heat capacity is continuous at Tc,q for a one-dimensional system but discontinuous at Tc,q for a two- or multi-dimensional system.

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.

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