Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.     

Casimir Effect at Finite Temperature in the Presence of Compactified Universal Extra Dimensions

We analyse the Casimir effect for parallel plates at finite temperature in the presence of compactified universal extra dimensions and analytically show the thermal corrections to the effect in detail. The Casimir effect for different sizes of universal extra dimensions is investigated to test the five-dimensional Kaluza-Klein theory.     

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization of multiple zeta function with one arbitrary exponent. We find a limit on the scale dimension like $\delta>\frac{1}{2}$ to keep the negative sign of the renormalized Casimir energy which is the difference between the regularized energy for two parallel plates and the one with no plates. We derive and calculate the Casimir force relating to the influence from the fractal additional compactified dimension between the parallel plates. The larger scale dimension leads to the greater revision on the original Casimir force. The two kinds of curves of Casimir force in the case of integer-numbered extra compactified dimension or fractal one are not superposition, which means that the Casimir force show whether the dimensionality of additional compactified space is integer or fraction.     

有限温度下的Casimir效应

利用路径积分量子化方法,计算出两个平行的、理想的金属板之间,在有限温度下自由的量子电磁场和内部费米子单圈图对Casimir力的贡献.     

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off A by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L∧ → ∞. There is a correction in the order of （L∧）^-2, when L∧ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale ∧^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.     

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off Λ by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit LΛ → ∞. There is a correction in the order of (LΛ)^-2, when LΛ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale Λ^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.     

Gravitational Casimir Effect at Finite Temperature

The energy-momentum tensor for the gravitoelectromagnetism-(GEM) theory in the real-time finite temperature field theory formalism is presented. Expressions for the Casimir energy and pressure at zero and finite temperature are obtained. An analysis of the Casimir effect for the GEM field is developed.     

Casimir Effect for Tachyonic Fields

In this paper we examine the Casimir effect for the case of a tachyonic field corresponding to particles with negative four-momentum squared, i.e., m² < 0. We consider here only the case of the one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of the Abel-Plana formula. Finally, the Casimir energy and Casimir force as the functions of distance are obtained. In order to compare the resulting formula with the standard one, we calculate the Casimir energy and Casimir force for massive, scalar field (m² > 0).     

Maxwell–Chern–Simons场的Casimir效应

利用约束理论对AbelMaxwell-Chem-Simons场进行路径积分量子化. 并利用复变函数论中Plana求和公式,计算(2+1)维空间中两个平行导线型边界的Casimir效应. 不引任何截断参数,而得出有限的解析表达式.     

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation.     

Casimir Effect for Dielectric Plates

We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of “evanescent mode” is discussed. The Lifshitz's formula is rederived using all the vacuum mode functions, which include the contribution of the ‘evanescent modes’. Only in the case of the perfect metallic plates will the evanescent modes become unimportant.     

The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Casimir force on a piston at finite temperature in Randall-Sundrum models

The Casimir effect for a three-parallel-plate system at finite temperature within the framework of five-dimensional Randall-Sundrum models is studied. In the case of the Randall-Sundrum model involving two branes we find that the Casimir force depends on the plate distance and temperature after one outer plate has been moved to a distant place. Further we discover that the sign of the reduced force is negative if the plate and piston are located close together, but the nature of reduced force becomes repulsive when the plate distance is not very small and finally the repulsive force vanishes with extremely large plate separation. A higher temperature causes a greater repulsive Casimir force. Within the framework of a one-brane scenario the reduced Casimir force between the piston and one plate remains attractive no matter how high the temperature is. It is interesting that a stronger thermal effect leads to a greater attractive Casimir force instead of changing the nature of the force.     

The Casimir effect and the fine structure constant

We consider the electron as a charged sphere that completely absorbs any radiation with wave number less than somek _m . The Casimir effect then provides a self stress which can balance the mutual repulsion of the distinct parts of the finite charge distribution. From this equilibrium condition and connecting, by quantum arguments, the value ofk _m to the radius of the electron, we obtain a good estimate for the value of the fine-structure constant.     

Letter: Trace Anomaly and Backreaction of the Dynamical Casimir Effect

The Casimir energy for massless scalar field which satisfies periodic boundary conditions in two-dimensional domain wall background is calculated by making use of general properties of renormalized stress-tensor. The line element of domain wall is time dependent, the trace anomaly which is the nonvanishing T for a conformally invariant field after renormalization, represent the back reaction of the dynamical Casimir effect.     

Dynamical Casimir Effect in a Cavity with a Resonantly Oscillating Boundary

We present analytical solutions describing quantized vacuum field in a one-dimensional cavity with one of its two mirrors fixed and another vibrating in simple harmonic form.These solutions are accurate up to the second order of the oscillating magnitude and they are uniformly valid for all time.We obtain the simple analytical expression for the energy density of the field which explicitly manifests that for a cavity vibrating at its q-th (q≥2) eigenfrequency, q traveling wave packets emerge in the finite part of the field energy density,and their amplitudes grow their widths shrink in time,representing a large concentration of energy.The finite part of the field energy density originating from the oscillations is shown to be proportional to the factor(q^2-1).     

Casimir Force of Squeezed Vacuum

The Casimir force of the quantized electromagnetic field in the squeezed vacuum state is calculated betweena pair of parallel perfectly conducting plates at zero temperature.     

Cosmological Particle Creation and Dynamical Casimir Effect

We compute particle creation for a real massive scalar field conformally coupled to a spatially closed Robertson–Walker space-time background, with time-dependent scale factor. This is a dynamical Casimir effect with moving boundaries.     

Casimir Force of Squeezed Vacuum

The Casimir force of the quantized electromagnetic field in the squeezed vacuum state is calculated between a pair of parallel perfectly conducting plates at zero temperature.