Recently it has been suggested that relativistic Bose gas of some type can be playing role in issues like dark matter, dark energy, and in some cosmological problems. In the current article we investigate one known exactly solvable model of three-dimensional statistical-mechanical model of relativistic Bose gas that takes into account the existence of both particles and antiparticles. We derive exact expressions for the behavior of the Casimir force for the system subjected to film geometry under periodic boundary conditions. We show that the Casimir force between the plates is attractive, monotonic as a function of the temperature scaling variable, with a scaling function that approaches at low temperatures a universal negative constant equal to the corresponding one for two-component three dimensional Gaussian system. The force decays with the distance in a power law near and below the bulk critical temperature $T_c$ of the Bose condensate and exponentially above $T_c$. We obtain closed form exact expression for the Casimir amplitude $Δ_{\rm Cas}^{\rm RBG} =-4ζ(3)/(5π)$. We establish the precise correspondence of the scaling function of the free energy of the model with the scaling functions of two other well-known models of statistical mechanics - the spherical model and the imperfect Bose gas model.
We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.
We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region the force decays exponentially fast when distance $D$ between the walls tends to infinity. When Bose-Einstein condensation point is approached the decay length in the exponential law diverges with critical exponent $ν_{IMP}=1…
The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length a…
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 $|{\bf p}|^α$ with $α\geq 2$ 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 $α\in\{4,6,8,\dots\}$ …
We study the Casimir effect for a 3-d system of ideal Bose gas in a slab geometry with Dirichlet boundary condition. We calculate the temperature($T$) dependence of the Casimir force below and above the Bose-Einstein condensation temperature($T_c$). At $T\le T_c$ the Casimir force vanishes as $[\frac{T}{T_c}]^{3/2}$. For $T\gtrsim T_c$ it weakly depends on temperature. For $T\gg T_c$ it vanishes exponentially. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of $\hbar$. At finite temperatures the Casimir force for o…
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…
We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of $\hbar$. At finite temperatures the Casimir force for our system depends on $\hbar$. For the calculation of Casimir force we consider only the Dirichlet boundary…
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<Tc (where Tc is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T>Tc, the Casimir force is an…
In a recent letter, Martin and Zagrebnov [Europhys. Lett., 73 (2006) 1] discussed the thermodynamic Casimir effect for the ideal Bose gas confined in a thin film. We point out that their findings can be expressed in terms of previous general results for the Casimir effect induced by confined critical fluctuations. This highlights the links between the Casimir effect in the contexts of critical phenomena and Bose-Einstein condensation.
We study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential $μ=0$ has the standard asymptotic form with universal Casimir terms.
We explore Casimir effect on an interacting Bose-Einstein condensate (BEC) inside a cylindrical tube. The Casimir force for the confined BEC comprises of (i) a mean-field part arising from the spatial inhomogeneity of the condensate order parameter, and (ii) a quantum fluctuation part arising from the confinement of Bogoliubov excitations in the condensate. Our analytical result predicts Casimir force on a cylindrical shallow of $^4$He well below the $λ$-point, and can be tested experimentally.
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 th…
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 l…
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.
The shift of density of Bose gas due to the mean field potential (MFP) and the Casimir effect is systematically investigated in the $d$-dimensional configuration space from the point of thermodynamic consideration. We show that, for $d=3$, the shift of density arises completely due to the Casimir effect and, the MFP remains totally ineffective regardless of the state, condensate or non-condensate. But for dimension $d>3$ the MFP plays an active role in shifting the density of Bose gas along with the Casimir interaction. The sign of density shift becomes positive in the present case. So, the co…
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 chemic…
We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T>T_c) the Casimir force decays exp…
The universal finite-size scaling function of the critical Casimir force for the three dimensional XY universality class with Dirichlet boundary conditions is determined using Monte Carlo simulations. The results are in excellent agreement with recent experiments on $^4$He Films at the superfluid transition and with available theoretical predictions.
We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is 1/D^2 with a non-universal amplitude. The next order correction is lnD/D^3. These observations remain in contrast with the decay law for both the periodic …
Tricritical Casimir forces in $^3\text{He}$ -$^4\text{He}$ wetting films are studied, within mean field theory, in therms of a suitable lattice gas model for binary liquid mixtures with short--ranged surface fields. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with $^4\text{He}$ and it allows, inter alia, for the occurrence of a vapor phase. As a result, the model facilitates the formation of wetting films, which provides a strengthened theoretical framework to describe available experimental data for tricritical …
Finite size effect in critical systems can be interpreted as universal Casimir forces. Here we compare the Casimir force for free, periodic and antiperiodic boundary conditions in the exactly calculable case of the Ising model in one and two dimensions. We employ a new procedure which allows us to calculate the Casimir force with periodic and antiperiodic boundary conditions analytically in a transparent manner. Quite interestingly, we find an attractive Casimir force for the case of periodic boundary condition but a repulsive Casimir force for the anti-periodic one.
Universal aspects of the thermodynamic Casimir effect in wetting films of 3He-4He mixtures near their bulk tricritical point are studied within suitable models serving as representatives of the corresponding universality class. The effective forces between the boundaries of such films arising from the confinement are calculated along isotherms at several fixed concentrations of 3He. Nonsymmetric boundary conditions impose nontrivial concentration profiles leading to repulsive Casimir forces which exhibit a rich behavior of the crossover between the tricritical point and the line of critical po…
Monte Carlo simulations based on an integration scheme for free energy differences is used to compute critical Casimir forces for three-dimensional Ising films with various boundary fields. We study the scaling behavior of the critical Casimir force, including the scaling variable related to the boundary fields. Finite size corrections to scaling are taken into account. We pay special attention to that range of surface field strengths within which the force changes from repulsive to attractive upon increasing the temperature. Our data are compared with other results available in the literature…
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 P. A. and Zagrebnov V. A., Europhys. Lett., 73 (2006) 15.). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above …
Measurements of Casimir effects in $^4$He films in the vicinity of the bulk superfluid transition temperature $T_λ$ have been carried out, where changes in the film thickness and the superfluid density are both monitored as a function of temperature. The Kosterlitz-Thouless superfluid onset temperature in the film is found to occur just as the Casimir dip in the film thickness from critical fluctuations becomes evident. Additionally, a new film-thickening effect is observed precisely at $T_λ$ when the temperature is swept extremely slowly. We propose that this is a non-universal Casimir effect…
Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when size of the thermal vortex loops is comparable to the film thickness, and the results for T < Tc are found to match very well with perturbative renormalization theories that have only been carried out for T > Tc. When applied to a high-Tc superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and bulk, and estimates show that this may be readily measurable.
The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it 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 …
Recent experiments on the wetting of $^{4}$He have shown that the film becomes thinner at the $λ$ transition, and in the superfluid phase. The difference in thickness above and below the transition has been attributed to a Casimir interaction which is a consequence of a broken continuous symmetry in the bulk superfluid. However, the observed thinning of the film is larger than can be accounted by this Casimir force. We show that surface fluctuations give rise to an additional force, similar in form but larger in magnitude, which may explain the observations.
We study the thermodynamic Casimir force for films with various types of boundary conditions and the bulk universality class of the three-dimensional Ising model. To this end we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. In particular, we employ the exchange or geometric cluster cluster algorithm [J.R. Heringa and H. W. J. Blöte, Phys. Rev. E 57, 4976 (1998)]. In a previous work we demonstrated that this algorithm allows to compute the thermodynamic Casimir force for the plate-sphere geometry efficiently. It turns out that also for the film g…
We calculate the Casimir stresses in a thin layer of active fluid with nematic order. By using a stochastic hydrodynamic approach for an active fluid layer of finite thickness $L$, we generalize the Casimir stress for nematic liquid crystals in thermal equilibrium to active systems. We show that the active Casimir stress differs significantly from its equilibrium counterpart. For contractile activity, the active Casimir stress, although attractive like its equilibrium counterpart, diverges logarithmically as $L$ approaches a threshold of the spontaneous flow instability from below. In contrast…
We have extended the mean field calculation of Zandi et al [1] and have obtained an approximate mathematical expression for the Casimir scaling function, which if extrapolated to the domain $π^2\ge-y\ge 0$, becomes surprisingly similar to that obtained experimentally by Ganshin et al [2]. The extrapolated scaling function can be regarded as a proposed fitting function, that appears to agree better with the experiments [2] in D=3, than the exact mean field result of Zandi et al [1].
Recently V. A. Yampol'skii, S. Savel'ev, Z. A. Mayselis, S. S. Apostolov, and F. Nori [Phys. Rev. Lett., v.101, 096803 (2008),arXiv:0712.1395] claimed that the Casimir force between a thin metal film described by the Drude model and an ideal metal semispace can decrease with temperature whereas for bulk samples the Casimir force increases with temperature. On this basis the experimental observation of the decreasing temperature dependence of the Casimir force magnitude between a film and a bulk ideal metal was proposed. We demonstrate that, contrary to what is claimed by the authors, the magni…
Thermodynamic Casimir forces of film systems in the O$(n)$ universality classes with Dirichlet boundary conditions are studied below bulk criticality. Substantial progress is achieved in resolving the long-standing problem of describing analytically the pronounced minimum of the scaling function observed experimentally in $^4$He films $(n=2)$ by R. Garcia and M.H.W. Chan, Phys. Rev. Lett. ${\bf 83}, 1187 \;(1999)$ and in Monte Carlo simulations for the three-dimensional Ising model ($n=1$) by O. Vasilyev et al., EPL ${\bf 80}, 60009 \;(2007)$. Our finite-size renormalization-group approach yie…
We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.
When masless excitations are limited or modified by the presence of material bodies one observes a force atcing between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the ph…
We present an analytical solution of the Ginzburg's $Ψ$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point, and we revisit the corresponding experiments in light of our findings. We find reasonably good agreement between the $Ψ$-theory predictions and the experimental data. Our calculated force is attractive, and the largest absolute value of the scaling function is $1.848$, while experiment yields $1.30$. The position of the extremum is predicted to be at $x=(L/ξ_0)(T/T_λ-1)^{1/ν}=π$, while experiment is consiste…
We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center of mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in details and various regimes (van der Waals-London, Casimir-Polder and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for…
We study the Casimir effect in the vicinity of a quantum critical point. As a prototypical system we analyze the $d$-dimensional imperfect (mean-field) Bose gas enclosed in a slab of extension $L^{d-1}\times D$ and subject to periodic boundary conditions. The thermodynamic state is adjusted so that $L\ggλ\gg D\ggł_{mic}$, where $λ\sim T^{-1/2}$ is the thermal de Broglie length, and $l_{mic}$ denotes microscopic lengthscales. Our exact analysis indicates that the Casimir force in the above specified regime is generically repulsive and decays either algebraically or exponentially, with a non-uni…
The limit n to infinity of the classical O(n) phi^4 model on a 3d film with free surfaces is studied. Its exact solution involves a self-consistent 1d Schrödinger equation, which is solved numerically for a partially discretized as well as for a fully discrete lattice model. Numerically exact results are obtained for the scaled Casimir force at all temperatures. Obtained via a single framework, they exhibit all relevant qualitative features of the thermodynamic Casimir force known from wetting experiments on Helium-4 and Monte Carlo simulations, including a pronounced minimum below the bulk cr…
In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here, we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the OP profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Our analytical resul…
The confinement of long-ranged critical fluctuations in the vicinity of second-order phase transitions in fluids generates critical Casimir forces acting on confining surfaces or among particles immersed in a critical solvent. This is realized in binary liquid mixtures close to their consolute point $T_{c}$ which belong to the universality class of the Ising model. The deviation of the difference of the chemical potentials of the two species of the mixture from its value at criticality corresponds to the bulk magnetic filed of the Ising model. By using Monte Carlo simulations for this latter r…
In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean fi…
We consider the effective pseudo-Casimir interaction forces mediated by a nematic liquid-crystalline film bounded by two planar surfaces, one of which imposes a random (disordered) distribution of the preferred anchoring axis in the so-called easy direction. We consider both the case of a quenched as well as an annealed disorder for the easy direction on the disordered surface and analyze the resultant fluctuation-induced interaction between the surfaces. In the case of quenched disorder, we show that the disorder effects appear additively in the total interaction and are dominant at intermedi…
The contact value theorem for Coulomb gases in planar or film-like geometries is derived using a Hamiltonian field theoretic representation of the system. The case where the film is enclosed by a material of different dielectric constant to that of the film is shown to contain an additional Casimir-like term which is generated by fluctuations of the electric potential about its mean-field value.
Recent experimental data for the complete wetting behavior of pure 4He and of 3He-4He mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses L upon approaching thermodynamically the lambda-transition and the tricritical end point, respectively, which can be attributed to critical Casimir forces f_C. We calculate the scaling functions vartheta of f_C within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of vartheta deduced from the experimental data and predi…
For the first time we present analytical results for the contribution of electromagnetic fluctuations into thermodynamic properties of modulated systems, like cholesteric or smectic liquid crystalline films. In the case of small dielectric anisotropy we have derived explicit analytical expressions for the chemical potential of such systems. Two limiting cases were specifically considered: (i) the Van der Waals (VdW) limit, i.e., in the case when the retardation of the electromagnetic interactions can be neglected; and (ii) the Casimir limit, i.e. when the effects of retardation becomes conside…
Random (disordered) components in the surface anchoring of the smectic-A liquid crystalline film in general modify the thermal pseudo-Casimir interaction. Anchoring disorder of the quenched type is in general decoupled from the thermal pseudo-Casimir force and gives rise to an additional disorder-generated interaction, in distinction to the annealed disorder, whose effect on the pseudo-Casimir force is non-additive. We consider the effects of the surface anchoring disorder by assuming that one of the substrates of the film is contaminated by a disorder source, resulting in a Gaussian-weighted …
Using analytic and numerical approaches, we study the spatio-temporal evolution of a conserved order parameter of a fluid in film geometry, following an instantaneous quench to the critical temperature $T_c$ as well as to supercritical temperatures. The order parameter dynamics is chosen to be governed by model B within mean field theory and is subject to no-flux boundary conditions as well as to symmetric surface fields at the confining walls. The latter give rise to critical adsorption of the order parameter at both walls and provide the driving force for the non-trivial time evolution of th…
Experiments on $^4$He films reveal an attractive Casimir-like force at the bulk $λ$-point, and in the superfluid regime. Previous work has explained the magnitude of this force at the $λ$ transition and deep in the superfluid region but not the substantial attractive force immediately below the $λ$-point. Utilizing a simple mean-field calculation renormalized by critical fluctuations we obtain an effective Casimir force that is qualitatively consistent with the scaling function $\vartheta$ obtained by collapse of experimental data.
We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg's $Ψ$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by $d=3$, $ν=2/3$ and $β=1/3$, where $d$ is the bulk spatial d…
We study the thermodynamic Casimir effect in thin films in the three dimensional XY universality class. To this end, we simulate the improved two component phi^4 model on the simple cubic lattice. We use lattices up to the thickness L_0=33. Based on the results of our Monte Carlo simulations we compute the universal finite size scaling function theta that characterizes the behaviour of the thermodynamic Casimir force in the neighbourhood of the critical point. We confirm that leading corrections to the universal finite size scaling behaviour due to free boundary conditions can be expressed by …
We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++, where all spins at the boundary are fixed to +1 and +-, where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1. An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to …
We discuss the relation of the specific heat, the energy density and the thermodynamic Casimir effect in the case of thin films in the three dimensional XY universality class. The finite size scaling function $θ(x)$ of the thermodynamic Casimir force can be expressed in terms of the scaling functions h'(x) and h(x) of the excess energy density and the excess free energy density. A priori these quantities depend on the reduced temperature t and the thickness L_0 of the film. However finite size scaling theory predicts that the scaling functions depend only on the combination x=t [L_0/ξ_0]^{1/ν}…
We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that Bose-Einstein(B-E) statistics needs a correction for finite system at ultralow temperatures. As a corrected statistics we introduced a Tsallis type of generalized B-E statistics. The condensate fraction calculated with this generalized B-E statistics, is satisfied well with the experimental result. In the third section we show how to apply the scaling theory in an inho…
On the example of the spherical model we study, as a function of the temperature $T$, the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry $\infty^{d-1}\times L$, where $2<d<4$ is the dimensionality of the system. We consider a system with nearest-neighbor anisotropic interaction constants $J_\parallel$ parallel to the film and $J_\perp$ across it. The model represents the $n\to\infty$ limit of O(n) models with antiperiodic boundary conditions applied across the finite dimension $L$ of the film. We observe that the Casimir amplitude $Δ_{\rm Casimir}(d|J_…
Systems described by an O(n) symmetrical $ϕ^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. A detailed renormalization-group (RG) study of the critical Casimir forces induced between the film's boundary planes by thermal fluctuations is presented for the case where the O(n) symmetry remains unbroken by the surfaces. The boundary planes are assumed to cause short-ranged disturbances of the interactions that can be modelled by standard surface contributions $\propto \bmϕ^2$ corresponding to subcritical or critical enhancement of the surface interac…
We investigate the three dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $α$ where $0 \le α\le π$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film---and the Casimir force it generates---as a function of the temperature $T$, th…
Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and XY universality classes. Several surface universality classes of the confining surfaces are considered, some of which are relevant for recent experiments. A novel approach introduced previously EPL 80, 60009 (2007), based inter alia on an integration scheme of free energy differences, is utilized to compute the universal scaling functions of the critical …
