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

Journal of Experimental and Theoretical Physics

The Casimir Effect in Bose–Einstein Condensate Mixtures Confined by a Parallel Plate Geometry in the Improved Hartree–Fock Approximation

Nguyễn Văn Thụ

Published Aug 1, 2022• 2 citations
Publisher

Abstract

Abstract By means of the Cornwall–Jackiw–Tomboulis effective potential formalism, the Casimir effect in binary Bose–Einstein condensate mixtures is investigated. The study conditions are that the mixtures are confined between two parallel plates at zero temperature and within the improved Hartree–Fock approximation featuring higher-order terms in the momentum integrals. Our results show that both effective masses and order parameters strongly depend on the distance between the two plates. The Casimir energy and resulting Casimir force are scrutinized, confirming that the contribution of the higher-order terms of the momentum integrals is significant. Importantly, the Casimir force is proved to be non-zero in limit of the full strong segregation, which is an acceptable answer for the controversial problem.

DOI
10.1134/s1063776122080131

Related papers

Finite-size effect on Bose–Einstein condensate mixtures in improved Hartree–Fock approximation

Nguyễn Văn Thụ, Luong Thi Theu

By means of Cornwal–Jackiw–Tomboulis effective action approach we considered the finite-size effect on Bose–Einstein condensate mixtures confined between two parallel palates. Keeping upto double-bubble approximation and taking into account the conservation of Goldstone boson, our results are quite different from those in previous works within one-loop approximation. The order parameters strongly depend on the distance between palates and can be expressed via the correction terms. The Casimir force is also considered.

arXiv:1809.10930•International Journal of Modern Physics B•Apr 29, 2019•11 citations

Casimir forces in Bose–Einstein condensates: finite-size effects in three-dimensional rectangular cavities

Ariel Edery

The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.

arXiv:hep-th/0510238•Journal of Statistical Mechanics Theory and Experiment•Jun 8, 2006•27 citations

Condensate Density of a Bose Gas Confined between Two Parallel Plates in Canonical Ensemble within Improved Hartree-Fock Approximation

Nguyễn Văn Thụ

By means of Cornwall-Jackiw-Tomboulis (CJT) effective action approach, the condensate density of a dilute Bose gas is investigated in the canonical ensemble. Our results show that the condensate density is proportional to a half-integer power law of the s-wave scattering length and distance between two plates. Apart from that, these quantities also depend on the particle number and area of each plate.

VNU Journal of Science Mathematics - Physics•Oct 7, 2020•0 citations

Casimir energy of a BEC: from moderate interactions to the ideal gas

Jürgen Schiefele, Carsten Henkel

Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose–Einstein condensate (BEC), we derive a renormalized expression for the zero-temperature Casimir energy of a BEC confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal BEC. For the weakly interacting case, reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.

arXiv:0809.1816•Journal of Physics A Mathematical and Theoretical•Dec 17, 2008•27 citations

Density of condensates of two-component Bose-Einstein condensates restricted between two planar walls

Nguyễn Văn Thụ, Phạm Thế Song, Nguyen Thi Le

Abstract The density of condensates of a binary mixture of Bose gases restricted by two parallel planar walls is investigated within the framework of Cornwal-Jackiw-Tomboulis effective action approach in improved Hartree-Fock approximation. It results that the density of condensates strongly depend not only on the distance between two walls but also on the interspecies interaction strength and they are equal their expectation values of the field operators after adding a term associated with the quantum fluctuations.

Journal of Physics Conference Series•May 1, 2021•3 citations

DENSITY OF CONDENSATE OF WEAKLY INTERACTING BOSE GAS CONFINED BETWEEN TWO HARD WALLS IN IMPROVED HARTREE-FOCK APPROXIMATION

Nguyễn Văn Thụ

By means of the Cornwall-Jackiw-Tomboulis effective potential, the condensate density of a weakly interacting Bose gas confined between two hard walls is investigated within an improved Hartree-Fock approximation (IHF). Our results show that the condensate density in an IHF approximation is always bigger than the one in a double-bubble approximation and that the condensate density strongly depends on the distance between two walls as well as the gas parameter.

Dalat University Journal of Science•May 4, 2020•1 citation
Abstract By means of the Cornwall–Jackiw–Tomboulis effective potential formalism, the Casimir effect in binary Bose–Einstein condensate mixtures is investigated. The study conditions are that the mixtures are confined between two parallel plates at zero temperature and within the improved Hartree–Fock approximation featuring higher-order terms in the momentum integrals. Our results show that both effective masses and order parameters strongly depend on the distance between the two plates. The Casimir energy and resulting Casimir force are scrutinized, confirming that the contribution of the higher-order terms of the momentum integrals is significant. Importantly, the Casimir force is proved to be non-zero in limit of the full strong segregation, which is an acceptable answer for the controversial problem.
By means of Cornwal–Jackiw–Tomboulis effective action approach we considered the finite-size effect on Bose–Einstein condensate mixtures confined between two parallel palates. Keeping upto double-bubble approximation and taking into account the conservation of Goldstone boson, our results are quite different from those in previous works within one-loop approximation. The order parameters strongly depend on the distance between palates and can be expressed via the correction terms. The Casimir force is also considered.
The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.
Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose–Einstein condensate (BEC), we derive a renormalized expression for the zero-temperature Casimir energy of a BEC confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal BEC. For the weakly interacting case, reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.
Abstract The density of condensates of a binary mixture of Bose gases restricted by two parallel planar walls is investigated within the framework of Cornwal-Jackiw-Tomboulis effective action approach in improved Hartree-Fock approximation. It results that the density of condensates strongly depend not only on the distance between two walls but also on the interspecies interaction strength and they are equal their expectation values of the field operators after adding a term associated with the quantum fluctuations.