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:2103.13502 · Journal of Statistical Mechanics Theory and Experiment

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

Marek Napiórkowski, Pawel Jakubczyk

Published Aug 1, 2021• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1742-5468/ac0c73

Related papers

Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices

Maciej Łebek, Paweł Jakubczyk

We consider the Bose gas on a $d$-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature $T$. We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this phenomenon. Subsequently we study the thermodynamic Casimir effect occurring in this system. We compute the exact profile of the scaling function for the Casimir energy. As an effect of strongly anisotropic scale invariance, the Casimir force below or at the critical temperature ${T}_{c}$ may be repulsive even for periodic boundary conditions. The corresponding Casimir amplitude is universal only in a restricted sense, and the power law governing the decay of the Casimir interaction becomes modified. We also demonstrate that, under certain circumstances, the scaling function is constant for sufficiently large values of the scaling variable, and in consequence is not an analytical function. At $T>{T}_{c}$ the Casimir-like interactions reflect the structure of the correlation function, and, for certain orientations of the confining walls, show exponentially damped oscillatory behavior so that the corresponding force is attractive or repulsive depending on the distance.

arXiv:2003.07458•Physical Review A•Jul 29, 2020•20 citations

Variance of the Casimir force in an ideal Bose gas

Marek Napiórkowski, Marcin Piotr Pruszczyk

Abstract We consider an ideal Bose gas enclosed in a d -dimensional slab of thickness D . Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab’s walls. The variance evaluated per unit wall area is shown to decay like Δ var / D for large D . The amplitude Δ var is a non-universal function of two scaling variables λ / ξ and D / ξ , where λ is the thermal de Broglie wavelength and ξ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose–Einstein condensate the amplitude Δ var retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form ( D / L ) d − 1 2 ( D / λ ) d / 2 , where L is the linear size of the wall.

arXiv:2205.06797•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2022•3 citations

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

Ekrem Aydıner

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.

arXiv:1504.01214•Apr 6, 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

Thermal Casimir effect in the spin–orbit coupled Bose gas

Marek Napiórkowski, Paweł Jakubczyk

Abstract We study the thermal Casimir effect in ideal Bose gases with spin–orbit (S–O) coupling of Rashba type below the critical temperature for Bose–Einstein condensation. In contrast to the standard situation involving no S–O coupling, the system exhibits long-ranged Casimir forces in both two and three dimensions ( d = 2 and d = 3). We identify the relevant scaling variable involving the ratio D / ν of the separation between the confining walls D and the S–O coupling magnitude ν . We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases, the resulting Casimir force is attractive and the S–O coupling ν has impact on its magnitude. In d = 3 the exponent governing the decay of the Casimir force becomes modified by the presence of the S–O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In d = 2 the obtained Casimir force displays a singular behavior in the limit of vanishing ν .

arXiv:2510.26240•Journal of Statistical Mechanics Theory and Experiment•Mar 1, 2026•0 citations

Repulsive Casimir force in Bose–Einstein Condensate

Mir Mehedi Faruk, Shovon Biswas

Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.

arXiv:1712.08200•Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2018•17 citations
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.
We consider the Bose gas on a ddd-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature TTT. We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this phenomenon. Subsequently we study the thermodynamic Casimir effect occurring in this system. We compute the exact profile of the scaling function for the Casimir energy. As an effect of strongly anisotropic scale invariance, the Casimir force below or at the critical temperature Tc{T}_{c}Tc​ may be repulsive even for periodic boundary conditions. The corresponding Casimir amplitude is universal only in a restricted sense, and the power law governing the decay of the Casimir interaction becomes modified. We also demonstrate that, under certain circumstances, the scaling function is constant for sufficiently large values of the scaling variable, and in consequence is not an analytical function. At T>TcT>{T}_{c}T>Tc​ the Casimir-like interactions reflect the structure of the correlation function, and, for certain orientations of the confining walls, show exponentially damped oscillatory behavior so that the corresponding force is attractive or repulsive depending on the distance.
Abstract We consider an ideal Bose gas enclosed in a d -dimensional slab of thickness D . Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab’s walls. The variance evaluated per unit wall area is shown to decay like Δ var / D for large D . The amplitude Δ var is a non-universal function of two scaling variables λ / ξ and D / ξ , where λ is the thermal de Broglie wavelength and ξ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose–Einstein condensate the amplitude Δ var retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form ( D / L ) d − 1 2 ( D / λ ) d / 2 , where L is the linear size of the wall.
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.
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.
Abstract We study the thermal Casimir effect in ideal Bose gases with spin–orbit (S–O) coupling of Rashba type below the critical temperature for Bose–Einstein condensation. In contrast to the standard situation involving no S–O coupling, the system exhibits long-ranged Casimir forces in both two and three dimensions ( d = 2 and d = 3). We identify the relevant scaling variable involving the ratio D / ν of the separation between the confining walls D and the S–O coupling magnitude ν . We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases, the resulting Casimir force is attractive and the S–O coupling ν has impact on its magnitude. In d = 3 the exponent governing the decay of the Casimir force becomes modified by the presence of the S–O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In d = 2 the obtained Casimir force displays a singular behavior in the limit of vanishing ν .
Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.