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.

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.

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.

Bose–Einstein condensation at different temperatures below the critical temperature

2018 ◽  
Vol 32 (17) ◽  
pp. 1850194 ◽  
Author(s):  
Abhishek Das
Keyword(s):  
Critical Temperature ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Different Temperatures ◽  
Bose Einstein

In this paper, we endeavor to show that the phenomenon of Bose–Einstein condensation can take place at discrete temperatures lower than the known critical temperature value.

BOSE–EINSTEIN CONDENSATION OF PARTICLES TRAPPED IN A BOUNDED HARMONIC POTENTIAL

2001 ◽  
Vol 15 (15) ◽  
pp. 2169-2191 ◽  
Author(s):  
SHALINI LUMB ◽  
S. K. MUTHU
Keyword(s):  
Finite Number ◽  
Specific Heat ◽  
Temperature Curve ◽  
Harmonic Potential ◽  
Einstein Condensation ◽  
Condensate Fraction ◽  
Eigenvalue Spectrum ◽  
Heat Temperature ◽  
Bose Einstein Condensation ◽  
Bose Einstein

The behavior of a finite number of bosons trapped in a bounded harmonic potential is investigated. The eigenvalue spectrum is worked out numerically for three different sizes of the trap. The condensate fraction is determined and is found to increase suddenly below a certain temperature which is a characteristic signature of BEC. The specific heat-temperature curve also shows a peak, with the maximum shifting to lower values and occurring at higher temperatures, as the size of the assembly is reduced.

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