arXiv subjects

L. P. Teo

Publications and source records attributed to L. P. Teo.

At least 37 records · Page 2Linked to original sources

arXiv2011

First analytic correction to the proximity force approximation in the Casimir effect between two parallel cylinders

We consider the small separation asymptotic expansions of the Casimir interaction energy and the Casimir interaction force between two parallel cylinders. The leading order terms and the next-to-leading order terms are computed analytically. Four combinations of boundary conditions are considered, which are Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), Dirichlet-Neumann (DN) and Neumann-Dirichlet (ND). For the case where one cylinder is inside another cylinder, the computations are shown in detail. In this case, we restrict our attention to the situation where the cylinders are strictly eccentric and the distance between the cylinders $d$ is much smaller than the distance between the centers of the cylinders. The computations for the case where the two cylinders are exterior to each other can be done in the same way and we only present the results, which turn up to be similar to the results for the case where one cylinder is inside another except for some changes of signs. In all the scenarios we consider, the leading order terms are of order $d^{-7/2}$ and they agree completely with the proximity force approximations. The results for the next-to-leading order terms are new. In the limiting case where the radius of the larger cylinder approaches infinity, the well-known results for the cylinder-plate configuration with DD or NN boundary conditions are recovered.

quant-ph↗

arXiv2011

Casimir interaction between two concentric cylinders at nonzero temperature

We study the finite temperature Casimir interaction between two concentric cylinders. When the separation between the cylinders is much smaller than the radii of the cylinders, the asymptotic expansions of the Casimir interaction are derived. Both the low temperature and the high temperature regions are considered. The leading terms are found to agree with the proximity force approximations. The low temperature leading term of the temperature correction is also computed and it is found to be independent of the boundary conditions imposed on the larger cylinder.

quant-ph↗

arXiv2011

Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is $M^{p+1}\times T^q$ which has $q$ dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature regardless of the boundary conditions assumed on the compact torus. The asymptotic limits of the Casimir force in the small plate separation limit are also obtained.

hep-th↗

arXiv2011

Casimir interaction of concentric spheres at finite temperature

We consider the finite temperature Casimir effect between two concentric spheres due to the vacuum fluctuations of the electromagnetic field in the $(D+1)$-dimensional Minkowski spacetime. Different combinations of perfectly conducting and infinitely permeable boundary conditions are imposed on the spheres. The asymptotic expansions of the Casimir free energies when the dimensionless parameter $\vep$, the ratio of the distance between the spheres to the radius of the smaller sphere, is small are derived in both the high temperature region and the low temperature region. It is shown that the leading terms agree with those obtained using the proximity force approximation, which are of order $T\vep^{1-D}$ in the high temperature region and of order $\vep^{-D}$ in the low temperature region. Some universal structures are observed in the next two correction terms. The leading terms of the thermal corrections in the low temperature region are also derived. They are found to be finite when $\vep\rightarrow 0^+$, and are of order $T^{D+1}$.

quant-ph↗

arXiv2011

Casimir interaction between a cylinder and a plate at finite temperature: Exact results and comparison to proximity force approximation

We study the finite temperature Casimir interaction between a cylinder and a plate using the exact formula derived from the Matsubara representation and the functional determinant representation. We consider the scalar field with Dirichlet and Neumann boundary conditions. The asymptotic expansions of the Casimir energy and the Casimir force when the separation $a$ between the cylinder and the plate is small are derived. As in the zero temperature case, it is found that the leading terms of the Casimir energy and the Casimir force agree with those derived from the proximity force approximation when $rT\gg 1$, where $r$ is the radius of the cylinder. When $aT\ll 1\ll rT$ (the medium temperature region), the leading term of the Casimir energy is of order $T^{5/2}$ whereas for the Casimir force, it is of order $T^{7/2}$. In this case, the leading terms are independent of the separation $a$. When $1\ll aT\ll rT$ (the high temperature region), the dominating terms of the Casimir energy and the Casimir force come from the zeroth Matsubara frequency. In this case, the leading terms are linear in $T$, but for the energy, it is inversely proportional to $a^{3/2}$, whereas for the force, it is inversely proportional to $a^{5/2}$. The first order corrections to the proximity force approximations in different temperature regions are computed using perturbation approach. In the zero temperature case, the results agree with those derived in [Bordag, Phys. Rev. D \textbf{73}, 125018 (2006)].

quant-ph↗

arXiv2011

Casimir Effect Associated with Fractional Klein-Gordon Field

This paper gives a brief review on the recent work on fractional Klein-Gordon fields, in particular on the Casimir effect associated to fractional Klein-Gordon fields in various geometries and boundary conditions. New results on Casimir piston due to a fractional Klein-Gordon massive field are given.

math-ph↗

arXiv2011

Electromagnetic Casimir piston in higher dimensional spacetimes

We consider the Casimir effect of the electromagnetic field in a higher dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the 4-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder with the same cross section is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $\mathcal{N}$, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the $(4+n)$-dimensional Minkowski spacetime. However, if the size of $\mathcal{N}$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1+h/2$ times the Casimir force on a pair of large parallel plates in the 4-dimensional Minkowski spacetime, where $h$ is the first Betti number of $\mathcal{N}$. In the limit the manifold $\mathcal{N}$ vanishes, one does not obtain the Casimir force in the 4-dimensional Minkowski spacetime if $h$ is nonzero.

hep-th↗

arXiv2010

The Casimir interaction of a massive vector field between concentric spherical bodies

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, the are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.

quant-ph↗

arXiv2010

Casimir effect of massive vector fields

We study the Casimir effect due to a massive vector field in a system of two parallel plates made of real materials, in an arbitrary magnetodielectric background. The plane waves satisfying the Proca equations are classified into transverse modes and longitudinal modes which have different dispersion relations. Transverse modes are further divided into type I and type II corresponding to TE and TM modes in the massless case. For general magnetodielectric media, we argue that the correct boundary conditions are the continuities of $\mathbf{H}_{\parallel}, ϕ, \mathbf{A}$ and $\pa_xA_x$, where $x$ is the direction normal to the plates. Whereas there are type I transverse modes that satisfy all the boundary conditions, it is impossible to find type II transverse modes or longitudinal modes that satisfy all the boundary conditions. To circumvent this problem, type II transverse modes and longitudinal modes have to be considered together. We call the contribution to the Casimir energy from type I transverse modes as TE contribution, and the contribution from the superposition of type II transverse modes and longitudinal modes as TM contribution. Their massless limits give respectively the TE and TM contributions to the Casimir energy of a massless vector field. The limit where the plates become perfectly conducting is discussed in detail. For the special case where the background has unity refractive index, it is shown that the TM contribution to the Casimir energy can be written as a sum of contributions from two different types of modes, corresponding to type 2 discrete modes and type 3 continuum modes discussed by Barton and Dombey \cite{1}. For general background, this splitting does not work. The limit where both plates become infinitely permeable and the limit where one plate becomes perfectly conducting and one plate becomes infinitely permeable are also investigated.

quant-ph↗

arXiv2010

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.

hep-th↗

arXiv2010

Casimir force in noncommutative Randall-Sundrum models revisited

We propose another method to compute the Casimir force in noncommutative Randall-Sundrum braneworld model considered by K. Nouicer and Y. Sabri recently. Our method can be used to compute the Casimir force to any order in the noncommutative parameter. Contrary to the claim made by K. Nouicer and Y. Sabri that repulsive Casimir force can appear in the first order approximation, we show that the Casimir force is always attractive at any order of approximation.

hep-th↗

arXiv2010

Finite Temperature Casimir Effect in the Presence of Extra Dimensions

We consider the finite temperature Casimir force acting on two parallel plates in a closed cylinder with the same cross section of arbitrary shape in the presence of extra dimensions. Dirichlet boundary conditions are imposed on one plate and fractional Neumann conditions with order between zero (Dirichlet) and one (Neumann) are imposed on the other plate. Formulas for the Casimir force show that it is always attractive for Dirichlet boundary conditions, and is always repulsive when the fractional order is larger than 1/2. For some fractional orders less than 1/2, the Casimir force can be either attractive or repulsive depending on the size of the internal manifold and temperature.

hep-th↗

arXiv2010

Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities

Eigenmodes of electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE modes and one polarization for TM modes, giving rise to a total of (D-1) polarizations. In case of a D-dimensional ball, the eigenfrequencies of electromagnetic field with perfectly conducting boundary condition coincides with the eigenfrequencies of gauge one-forms with relative boundary condition; whereas the eigenfrequencies of electromagnetic field with infinitely permeable boundary condition coincides with the eigenfrequencies of gauge one-forms with absolute boundary condition. Casimir energy for a D-dimensional spherical shell configuration is computed using both cut-off regularization and zeta regularization. For a double spherical shell configuration, it is shown that the Casimir energy can be written as a sum of the single spherical shell contributions and an interacting term, and the latter is free of divergence. The interacting term always gives rise to an attractive force between the two spherical shells. Its leading term is the Casimir force acting between two parallel plates of the same area, as expected by proximity force approximation.

hep-th↗

arXiv2010

Casimir Piston of Real Materials and its Application to Multi-Layer Models

In this article, we derive the formula for the Casimir force acting on a piston made of real material moving inside a perfectly conducting rectangular box. It is shown that by taking suitable limits, one recovers the formula for the Casimir force acting on a perfectly conducting piston or an infinitely permeable piston. Lifshitz formula for finite temperature Casimir force acting on parallel plates made of real materials is re-derived by considering the five-layer model in the context of piston approach. It is observed that the divergences of the Casimir force will only cancel under certain conditions, for example, when the regions separated by the plates are filled with media of the same refractive index.

hep-th↗

arXiv2009

Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models

In this article, we derive the finite temperature Casimir force acting on a pair of parallel plates due to a massless scalar field propagating in the bulk of a higher dimensional brane model. In contrast to previous works which used approximations for the effective masses in deriving the Casimir force, the formulas of the Casimir force we derive are exact formulas. Our results disprove the speculations that existence of the warped extra dimension can change the sign of the Casimir force, be it at zero or any finite temperature.

hep-th↗

arXiv2009

Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions

In this article, we study the finite temperature Casimir effect for scalar field with Robin boundary conditions on two parallel plates in a background spacetime that has a compact internal manifold with arbitrary geometry. The finite temperature Casimir force acting on the plates is derived using the piston approach, with which we show that the divergences of the Casimir forces from the region between the plates and the region outside the plates cancel each other. The nature and asymptotic behaviors of the Casimir force at different limits such as small and large plate separation, low and high temperature, are studied in detail. The range of Robin coefficients where the Casimir force are always attractive or always repulsive are determined. There are also some range of the Robin coefficients where the Casimir force is shown to be attractive at small plate separation and repulsive at large plate separation, or vise versa.

hep-th↗

arXiv2009

Repulsive Casimir Force from Fractional Neumann Boundary Conditions

This paper studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a $d$-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.

hep-th↗

arXiv2009

Modeling Single-File Diffusion by Step Fractional Brownian Motion and Generalized Fractional Langevin Equation

Single-file diffusion behaves as normal diffusion at small time and as anomalous subdiffusion at large time. These properties can be described by fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann-Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as solution of fractional Langevin equation with zero damping. Various types of fractional Langevin equations and their generalizations are then considered to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where dissipative memory kernel is a Dirac delta function, a power-law function, and a combination of both of these functions, are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of the process that begins as ballistic motion.

cond-mat.stat-mech↗