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.     

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 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 Force in a One-Dimensional Cavity with Quasimode

We calculate the Casimir force between a perfect reflective wall and a semitransparent wall in the laser cavity. Using the Fox-Li quasimode theory to describe the electromagnetic field in the laser cavity, the vacuum energy and the Casimir force are calculated. We compare our results to the force in the ideal situation and find it smaller in the dissipative cavity. We also find that the Casimir force decreases with the increase of the wall-wall distance and the decay rate of the quasimodes in the laser cavity.     

Casimir Effect for Concentric Spheres in de Sitter Spacetime with Signature Change

We revisit the Casimir effect for two concentric spherical shells in de Sitter background with a new geometric configuration, namely Euclidean signature between and Lorentzian signature outside the spheres with different cosmological constants, for a massless scalar field satisfying Dirichlet boundary conditions on the spheres. It is shown that an extra constant pressure emerges due to this signature changing configuration. Some interesting aspects of this extra term are then discussed.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both flat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimir effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet ard Neumann boundary conditions are also discussed.     

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).     

Repulsive Casimir Force in a Cavity Comprising a Dielectric with Output Coupling

The Casimir force between a perfectly conducting wall and a dielectric wall in a cavity comprising a transparent dielectric with output coupling is investigated. By using full quantum theory, we obtain the analysis expression of the force, which shows that the interaction of the two walls in this system is always repulsive. And the value of the Casimir force varies with the field amplitude reflectivity and the cavity size.     

Repulsive Casimir Force in a Cavity Comprising a Dielectric with Output Coupling

The Casimir force between a perfectly conducting wall and a dielectric wall in a cavity comprising a transparent dielectric with output coupling is investigated. By using full quantum theory, we obtain the analysis expression of the force, which shows that the interaction of the two walls in this system is always repulsive. And the value of the Casimir force varies with the field amplitude reflectivity and the cavity size.     

Casimir Effect Under Two Dimensional Black Hole Spacetime Background with Global Monopole

A thin layer of the event horizon vicinity to the two-dimension black hole with a global monopole is considered as a system of the Casimir type. The energy-momentum tensor is derived in Boulware vacuum, Hartle-Hawking vacuum and Unruh vacuum respectively. The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions. Using the Wald's axioms, the result is got which is the same with the one derived by the usual regularized methods. Meanwhile, the energy, energy density, and pressure acting on the boundaries at the asymptotically flat background also are calculated too, and from the energy, Casimir force is derived. The Casimir energy and Casimir force are compared respectively in the background before and after radiation. PACS: 42.50.Lc.     

与额外维相关的膜宇宙模型

对引力场的能量\|动量和角动量守恒定律研究进展进行了总结。依此探讨了一般五维时空膜宇宙模型中的能量\|动量张量、 角动量张量以及它们的守恒定律。通过计算一个膜宇宙模型中的能动张量, 论证了该模型中“可见膜”上的引力非常弱, 这可认为是从引力的角度反映了规范层次问题。结果与一般的结论, 即引力系统总能量为零是一致的。同时, 分析了这个膜宇宙模型中的角动量张量, 计算了该模型中的总角动量, 讨论了暴涨Randall\|Sundren(RS)模型中的总角动量的一些性质。说明了在这类模型中总角动量的类空分量均为零, 这与普通RS模型是一样的。同时, 分析了RS模型中背景以及膜上的宇宙学常数, 发现在RS模型中五维背景宇宙学常数和两个膜上的真空能都能取它们的自然值。最后通过修改RS模型, 得到了一种可以产生很小的有效宇宙学常数的机制。We summarized both the general covariant energy\|momentum and angular momentum conservation law in the gravitational system and analyzed the general covariant energy\|momentum tensor of the gravitational system in general five\|dimensional cosmological in brane\|universe models. After calculating this energy\|momentum for the cosmological generalization of the Randall\|Sundrum(RS) model which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy. We also discussed the properties of the general covariant angular momentum in five\|dimensional brane-universe model. With calculation of the total angular momentum of this model, we analyzed the properties of the total angular momentum in the inflationary RS model. We pointed that the space-like components of the total angular momentum are zero while the others are non-zero, which agrees with the results from ordinary RS model. We also investigated the bulk cosmological constant and brane vacuum energies in RS model. We show that the five\|dimensional bulk cosmological constant and the vacuum energies of the two branes could take their natural values. Finally we argued how we can generate a small four-dimensional effective cosmological constant on the branes by modifying the original RS model.     

Five-dimensional Relativity with Energy as Extra Dimension

A Kaluza-Klein-like framework is developed infive-dimensional spaces in which the extra dimension isassumed to be the energy of physical processes and thefour-dimensional spacetime is endowed with anenergy-dependent metric. The detailed analysisof some classes of solutions of the (vacuum) Einsteinequations shows that the E = const. slices possessenergy-dependent four-dimensional metrics whichintriguingly reproduce the phenomenologicaldeformed metrics derived from theexperimental data on some physical phenomena ruled bythe four fundamental interactions (electromagnetic,weak, strong and gravitational). This extends previous results concerning theslowing down of clock rates in a gravitational field.Incidentally it is also shown that a special solution ofthe five-dimensional geodesics equation allowsto derive a sort of quantum-mechanicaltime-energy uncertainty relation.     

Dynamical Trajectories of Simple Mechanical Systems as Geodesics in Space with an Extra Dimension

We show the advantages of representing thedynamics of simple mechanical systems described by anatural Lagrangian, in terms of geodesics of aRiemannian (or pseudo-Riemannian) space with anadditional dimension. We demonstrate how generaltrajectories of simple mechanical systems can be putinto one-toone correspondence with the geodesics of asuitable manifold. Two different ways in which thegeometry of the configuration space can be obtained froma higher dimensional model are presented and compared:(1) by a straightforward projection, and (2) as a spacegeometry of a quotient space obtained by the action of the timelike Killing vectorgenerating a stationary symmetry of a background spacegeometry with an additional dimension. The second modelis more informative and coincides with the so-called optical model of the line-of-sight geometry. Onthe base of this model we study the behavior of nearbygeodesics to detect their sensitive dependence oninitial conditions — the key ingredient ofdeterministic chaos. The advantage of such a formulation isits invariant character.     

Casimir效应的另一种计算方法

利用Poisson求和公式和简单的正规化手续,给出了Casimir效应的另一种计算方法.     

Casimir effect for the sphere revisited

In a recent work Brevik et al. have offered formal proofs of two results which figure prominently in calculations of the Casimir pressure on a sphere. It is shown by means of simple counterexamples that each of those proofs is necessarily incorrect.     

On a theory of the Casimir effect

We develop a mathematically precise framework for the Casimir effect. A major role is played by Dietz's idea of identifying the Casimir energy as the regularization-independent Ramanujan sum of an asymptotic series. As an illustration, we treat two cases: parallel plates and the sphere. We finally discuss the open problem of the Casimir force for the cube. We propose an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive sign of the force.