Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.01214

Casimir force for geometrically confined ideal Bose gas in a harmonic-optical potential

Ekrem Aydıner

Published Apr 6, 2015• 0 citations
arXivHTMLPDF

Abstract

In this study, we have derived close form of the Casimir force for the non-interacting ideal Bose gas between two slabs in harmonic-optical lattice potential by using Ketterle and van Druten approximation. We find that Bose-Einstein condensation temperature $T_{c}$ is a critical point for different physical behavior of the Casimir force. We have shown that Casimir force of confined Bose gas in the presence of the harmonic-optical potential decays with inversely proportional to $d^{5}$ when $T\leq T_{c}$. However, in the case of $T>T_{c}$, it decays exponentially depends on separation $d$ of the slabs. Additionally we have discussed temperature dependence of Casimir force and importance of the harmonic-optical lattice potential on quantum critical systems, quantum phase transition and nano-devices.

DOI
10.48550/arxiv.1504.01214

Related papers

Casimir effect of an ideal Bose gas trapped in a generic power-law potential

Tongling Lin, Guozhen Su, Qiuping Alexandre Wang +1 more

The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T ⩽ T c (where T c is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T > T c , the Casimir force is an exponential decay function; and when T ≫ T c , the Casimir force vanishes.

arXiv:1209.3392•Europhysics Letters (EPL)•May 1, 2012•5 citations

Oscillating Casimir force of trapped Bose gas in electromagnetic field

Seyit Deniz Han, Ekrem Aydıner

In this study, we consider motion of the massive and charged Bose gas trapped in electric and magnetic fields between two parallel plates in the $x-y$ plane that are separated by a distance $d$ in the $z$ direction. We derive analytical expression of the grand canonical potential of the quantum particles by using of Ketterle and van Druten approximation. By evaluating canonical potential, we obtain Casimir potential and force at the Bose-Einstein condensation temperature $T_{c}$. We also show that Casimir force oscillates depends on distance $d$ for fixed parameters.

arXiv:1508.01040•Aug 5, 2015•0 citations

Bose condensation and the Casimir effects of an imperfect Bose gas in a d-dimensional configuration space

G.M. Bhuiyan

Abstract Some properties of an ideal gas of massive bosons in a mean field potential and, confined between two infinite parallel slabs in a d-dimensional configuration space are investigated systematically. Here, one particle density of states approach is employed to study the critical temperature, shift of density, Casimir effects and critical exponents, starting from the evaluation of the grand canonical free energy in d-dimension. We have found that, the shift of density, Casimir force and the critical temperature depend on the space dimensionality. But the Casimir force decays as an inverse power law of the distance between two slabs in the condensate and, decays exponentially in the non-condensed state situated very close to the point of phase transition. Specifically, this study enabled us to predict the shift of the density of boson in the excited states due to mean field potential, and also the dimensional dependence of the critical exponent. The form of the critical exponent is found to be 1 d − 2 for the imperfect Bose gas. This leads to a value of critical exponent 1 for d = 3. Most interestingly, in the limit when the mean field potential goes to zero the resulting expressions for the above properties coincide with those of the ideal Bose gas.

arXiv:1507.00673•Journal of Physics Conference Series•Jan 1, 2021•4 citations

Casimir Forces in Trapped Dilute Bose Gas Between Two Slabs

Xiao-Lu Yu, Ran Qi, Z. B. Li +1 more

We discuss a Casimir force due to zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC) with a strong harmonic trap. The results show that the presence of a strong harmonic trap changes the power law behavior of Casimir force due to the dimensional reduction effect. At finite temperature, we calculate Casimir force due to thermal fluctuation and find an exotic temperature dependent behavior in the first order term. Finally, we speculate some possible experimental realization and detection of the force in future experiments.

arXiv:0708.3132•Aug 23, 2007•0 citations

Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase

Ekrem Aydıner

Abstract In this study, ideal free and harmonically trapped Bose gases confined by two plates in the x–y‐plane in‐between distance d are considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti‐periodic boundary conditions. The Casimir force is then obtained for the Bose–Einstein condensate phase and for the non‐condensate phase . It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non‐condensate phase with the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.

Annalen der Physik•Jul 1, 2020•7 citations

Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality

Marek Napiórkowski, Pawel Jakubczyk

Abstract We analyze the thermodynamic Casimir effect occurring in a gas of non-interacting bosons confined by two parallel walls with a strongly anisotropic dispersion inherited from an underlying lattice. In the direction perpendicular to the confining walls, the standard quadratic dispersion is replaced by the term | p | α with α ⩾ 2 treated as a parameter. We derive a closed, analytical expression for the Casimir force depending on the dimensionality d and the exponent α , and analyze it for thermodynamic states in which the Bose–Einstein condensate is present. For α ∈ {4, 6, 8, …} the exponent governing the decay of the Casimir force with increasing distance between the walls becomes modified and the Casimir amplitude Δ α ( d ) exhibits oscillations of sign as a function of d . Otherwise, we find that Δ α ( d ) features singularities when viewed as a function of d and α . Recovering the known previous results for the isotropic limit α = 2 turns out to occur via a cancellation of singular terms.

arXiv:2103.13502•Journal of Statistical Mechanics Theory and Experiment•Aug 1, 2021•3 citations
In this study, we have derived close form of the Casimir force for the non-interacting ideal Bose gas between two slabs in harmonic-optical lattice potential by using Ketterle and van Druten approximation. We find that Bose-Einstein condensation temperature TcT_{c}Tc​ is a critical point for different physical behavior of the Casimir force. We have shown that Casimir force of confined Bose gas in the presence of the harmonic-optical potential decays with inversely proportional to d5d^{5}d5 when T≤TcT\leq T_{c}T≤Tc​. However, in the case of T>TcT>T_{c}T>Tc​, it decays exponentially depends on separation ddd of the slabs. Additionally we have discussed temperature dependence of Casimir force and importance of the harmonic-optical lattice potential on quantum critical systems, quantum phase transition and nano-devices.
The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T ⩽ T c (where T c is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T > T c , the Casimir force is an exponential decay function; and when T ≫ T c , the Casimir force vanishes.
In this study, we consider motion of the massive and charged Bose gas trapped in electric and magnetic fields between two parallel plates in the x−yx-yx−y plane that are separated by a distance ddd in the zzz direction. We derive analytical expression of the grand canonical potential of the quantum particles by using of Ketterle and van Druten approximation. By evaluating canonical potential, we obtain Casimir potential and force at the Bose-Einstein condensation temperature TcT_{c}Tc​. We also show that Casimir force oscillates depends on distance ddd for fixed parameters.
Abstract Some properties of an ideal gas of massive bosons in a mean field potential and, confined between two infinite parallel slabs in a d-dimensional configuration space are investigated systematically. Here, one particle density of states approach is employed to study the critical temperature, shift of density, Casimir effects and critical exponents, starting from the evaluation of the grand canonical free energy in d-dimension. We have found that, the shift of density, Casimir force and the critical temperature depend on the space dimensionality. But the Casimir force decays as an inverse power law of the distance between two slabs in the condensate and, decays exponentially in the non-condensed state situated very close to the point of phase transition. Specifically, this study enabled us to predict the shift of the density of boson in the excited states due to mean field potential, and also the dimensional dependence of the critical exponent. The form of the critical exponent is found to be 1 d − 2 for the imperfect Bose gas. This leads to a value of critical exponent 1 for d = 3. Most interestingly, in the limit when the mean field potential goes to zero the resulting expressions for the above properties coincide with those of the ideal Bose gas.
We discuss a Casimir force due to zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC) with a strong harmonic trap. The results show that the presence of a strong harmonic trap changes the power law behavior of Casimir force due to the dimensional reduction effect. At finite temperature, we calculate Casimir force due to thermal fluctuation and find an exotic temperature dependent behavior in the first order term. Finally, we speculate some possible experimental realization and detection of the force in future experiments.
Abstract In this study, ideal free and harmonically trapped Bose gases confined by two plates in the x–y‐plane in‐between distance d are considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti‐periodic boundary conditions. The Casimir force is then obtained for the Bose–Einstein condensate phase and for the non‐condensate phase . It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non‐condensate phase with the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.
Abstract We analyze the thermodynamic Casimir effect occurring in a gas of non-interacting bosons confined by two parallel walls with a strongly anisotropic dispersion inherited from an underlying lattice. In the direction perpendicular to the confining walls, the standard quadratic dispersion is replaced by the term | p | α with α ⩾ 2 treated as a parameter. We derive a closed, analytical expression for the Casimir force depending on the dimensionality d and the exponent α , and analyze it for thermodynamic states in which the Bose–Einstein condensate is present. For α ∈ {4, 6, 8, …} the exponent governing the decay of the Casimir force with increasing distance between the walls becomes modified and the Casimir amplitude Δ α ( d ) exhibits oscillations of sign as a function of d . Otherwise, we find that Δ α ( d ) features singularities when viewed as a function of d and α . Recovering the known previous results for the isotropic limit α = 2 turns out to occur via a cancellation of singular terms.