D. U. Matrasulov, Kh. T. Butanov, Kh. Yu. Rakhimov, F. C. Khanna, A. E. Santana
The Casimir effect for spherical geometry is calculated using generalized Thermofield Dynamics for the case of scalar field. Casimir force and Casimir pressure are presented. It is found that for high temperatures the Casimir force does change sign.
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A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F. C. Khanna and A. E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyse the energy-momentum tensor for the Casimir effect of a free massless fermion field in a $d$-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a 3-dimensional parallelepiped b…
It is shown that the recent criticism of Brevik et al. (hep-th/0004041) is in error.
By the thermofield dynamics (TFD) formalism we obtain the energy-momentum tensor for the Electromagnetism with Lorentz Breaking Even term of the Standard Model Extended (SME) Sector in a topology $S^{1}\times S^{1}\times R^{2}$. We carry out the compactification by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor, and the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and we remark the influence of the background in the traditional Casimir effect.
We use the thermofield dynamics (TFD) formalism to obtain the energy-momentum tensor for the Kalb-Ramond (KR) field in a topology $% S^{1}\times S^{1}\times R^{2}$. The compactification is carried out by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor. The expressions for the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and the results may be important for applications, as in cuprate superconductivity, for instance.
Calculations of the Casimir energy for spherical geometries which are based on integrations of the stress tensor are critically examined. It is shown that despite their apparent agreement with numerical results obtained from mode summation methods, they contain a number of serious errors. Specifically, these include (1) an improper application of the stress tensor to spherical boundaries, (2) the neglect of pole terms in contour integrations, and (3) the imposition of inappropriate boundary conditions upon the relevant propagators. A calculation which is based on the stress tensor and which av…
The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum-field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar field, the approach is extended to the electromagnetic field and the energy-momentum tensor is written via the Bogoliubov transformation. In this context, the Casimir effect is calculated for zero and non-zero temperature, and therefore it can be considered as a vacuum condensation effect of the electromagnetic field. This aspect opens an interesting perspective …
It is shown that recent criticism by C. R. Hagen (hep-th/9902057) questioning the validity of stress tensor treatments of the Casimir energy for space divided into two parts by a spherical boundary is without foundation.
In this work a generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermion counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F.C. Khanna and A.E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion system in a N-dimensional box in contact with a heat bath. As a particular situation we calculate the Casimir energy and pressure for the field in a 3-dimen…
Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical boundaries. It is assumed that the field obeys general Robin boundary conditions on bounding surfaces. The application of a variant of the generalized Abel-Plana formula allows to extract from the expectation values the contribution from single shells and to present the interference part in terms of exponentially convergent integrals. The vacuum forces acting on the…
We perform the matching required to compute the leading effective boundary contribution to the QED lagrangian in the presence of a conducting surface, once the electron is integrated out. Our result resolves a confusion in the literature concerning the interpretation of the leading such correction to the Casimir energy. It also provides a useful theoretical laboratory for brane-world calculations in which kinetic terms are generated on the brane, since a lot is known about QED near boundaries.
Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integr…
We calculate modifications to the scalar Casimir force between two parallel plates due to space-time non-commutativity. We devise a heuristic approach to overcome the difficulties of describing boundaries in non-commutative theories and predict that boundary corrections are of the same order as non-commutative volume corrections. Further, both corrections have the form of more conventional finite surface effects.
The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single plate with a slit in it, perpendicular plates separated by a gap, and two parallel plates, one of which has a long slit of large width, related to the case of one plate being semi-infinite. We develop a general formalism for studying such problems, based on the wavefunctional for the field in the gap between the plates. This formalism leads to a lower dimension…
Compact U(1) gauge theory in 3+1 dimensions possesses the confining phase, characterized by a linear raise of the potential between particles with opposite electric charges at sufficiently large inter-particle separation. The confinement is generated by condensation of Abelian monopoles at strong gauge coupling. We study the properties of monopoles and the deconfining order parameter in zero-temperature theory in the presence of ideally conducting parallel metallic boundaries (plates) usually associated with the Casimir effect. Using first-principle numerical simulations in compact U(1) lattic…
The effects of reflecting boundaries on vacuum electric field fluctuations are treated. The presence of the boundaries can enhance these fluctuations and possibly lead to observable effects. The electric field fluctuations lead to voltage fluctuations along the worldline of a charged particle moving perpendicularly to a pair of reflecting plates, These voltage fluctuations in turn lead to fluctuations in the kinetic energy of the particle, which may enhance the probability of quantum barrier penetration by the particle. A recent experiment by Moddel {\it et al} is discussed as a possible examp…
The regularized total Casimir energy in spacetimes with boundaries is not in general equal to the integral of the regularized energy density. This paradoxical phenomenon is most transparently analyzed in the simple example of a massless scalar field in 1+1 dimensions confined to a line element of length $L$ and obeying Dirichlet boundary conditions.
The vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with Dirichlet boundary conditions and for the electromagnetic field inside a wedge with a coaxial cylindrical boundary. In the case of the electromagnetic field perfectly conducting boundary conditions are assumed on the bounding surfaces. By using the Abel-Plana-type formula for the series over the zeros of the Bessel function, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry without a cylindrical bound…
Vacuum expectation values of the energy-momentum tensor and the Casimir forces are evaluated for scalar and electromagnetic fields in the geometry of two curved boundaries on background of the Robertson-Walker spacetime with negative spatial curvature. Robin boundary conditions are imposed in the case of the scalar field and perfect conductor boundary conditions are assumed for the electromagnetic field. We use the conformal relation between the Robertson-Walker and Rindler spacetimes and the corresponding results for two parallel plates moving with uniform proper acceleration through the Full…
We consider the Casimir energy in a geometry of an infinite magnetodielectric wedge closed by a circularly cylindrical, perfectly conducting arc embedded in another magnetodielectric medium, under the condition that the speed of light be the same in both media. An expression for the Casimir energy corresponding to the arc is obtained and it is found that in the limit where the reflectivity of the wedge boundaries tends to unity the finite part of the Casimir energy of a perfectly conducting wedge-shaped sheet closed by a circular cylinder is regained. The energy of the latter geometry possesse…
We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by $δ$-function potentials, so-called semitransparent boundaries. A finite expression for the Casimir energy corresponding to the arc and the presence of both semitransparent potentials is obtained, from which the torque on the sidewalls can be derived. The most interesting part of the calculation is the nontrivial nature of the angular mode functions. Numerical results are obtained which are closely analogous to those recently foun…
Classical and quantum field theory in a box with moving boundaries: A numerical study of the Dynamical Casimir Effect
本研究建立了含运动边界腔体内的量子标量场理论与静态Dirichlet边界声学度规场论的等价性，提出可用于任意边界轨迹的动力学卡西米尔效应粒子产生非微扰数值方法，并以1+1维无质量场为例验证，方法可扩展到有质量场和高维场景。
The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically the non-vanishing Casimir…
In this article we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We present a new regularization mechanism the piston offers. In our case regularization occurs explicitly at the Casimir energy density and not at the Casimir force level, as in usual pistons. We make use of boundary broken supersymmetry …
Field theoretic description of electromagnetic boundaries: The Casimir effect between dissimilar mirrors from external potentials
本文基于有效势耦合的半透明介电表面模型，精确求解两个不同镜面间的光子传播子修正，并据此计算单轴介电表面的 Casimir 能量及相互作用行为。
We study the finite temperature Casimir interactions on two parallel boundaries in the anti-de Sitter spacetime AdS$_{D+1}$ induced by the vacuum fluctuations of a massive fermionic field with MIT bag boundary conditions. As in the Minkowski spacetime, the Casimir interaction always tends to attract the two boundaries to each other at any temperature and for any mass. For bosonic fields, it is well known that the high temperature leading term of the Casimir interaction is linear in temperature. However, for fermionic fields, the Casimir interaction decays exponentially at high temperature due …
One-Loop Correction to the Casimir Energy in Lorentz-Violating $ϕ^4$ Theory with Rough Membrane Boundaries
本文计算了在3+1维时空中，具有粗糙表面的两个膜之间，有质量和无质量洛伦兹破缺标量场的卡西米尔能量的辐射修正，使用了位置依赖抵消项和盒子减除方案。
We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from accelerating boundaries. Applications are provided for objects with different shapes in various dimensions, and undergoing rotational or linear motion. Within this framework, photon generation is discussed in the context of a modulated optical mirror. For dispersive objects, we find general results solely in terms of the scattering matrix. Specifically, we discus…
Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of geometries. For the planar case a finite universal force is automatically found. For curved geometries formally divergent expressions are encountered which we argue are largely due to the divergent self-energy of the boundary contributing to the force. This idea is supported by computing…
The vacuum expectation values for the energy-momentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on spherically symmetric boundaries in D-dimensional space are investigated. The expressions are derived for the regularized vacuum energy density, radial and azimuthal stress components (i) inside and outside a single spherical surface and (ii) in the intermediate region between two concentric spheres. Regularization procedure is carried out by making use of the generalized Abel-Plana formula for the series over zeros of cylinder funct…
We discuss the quantization of sound waves in a fluid with a linear dispersion relation and calculate the quantum density fluctuations of the fluid in several cases. These include a fluid in its ground state. In this case, we discuss the scattering cross section of light by the density fluctuations, and find that in many situations it is small compared to the thermal fluctuations, but not negligibly small and might be observable at room temperature. We also consider a fluid in a squeezed state of phonons and fluids containing boundaries. We suggest that the latter may be a useful analog model …
We consider and review the emergence of singular energy densities and field fluctuations at sharp boundaries or point-like field sources in the vacuum. The presence of singular energy densities of a field may be relevant from a conceptual point of view, because they contribute to the self-energy of the system. They should also generate significant gravitational effects. We first consider the case of the interface between a metallic boundary and the vacuum, and obtain the structure of the singular electric and magnetic energy densities at the interface through an appropriate limit from a dielec…
Motivated by experiments in which moving boundaries are simulated by time-dependent properties of static systems, we discuss the model of a massless scalar field submitted to a time-dependent Robin boundary condition (BC) at a static mirror in 1+1 dimensions. Using a perturbative approach, we compute the spectral distribution of the created particles and the total particle creation rate, considering a thermal state as the initial field state.
Casimir effect in the planar setting is described using the boundary state formalism, for general partially reflecting boundaries. It is expressed in terms of the low-energy degrees of freedom, which provides a large distance expansion valid for general interacting field theories provided there is a non-vanishing mass gap. The expansion is written in terms of the scattering amplitudes, and needs no ultraviolet renormalization. We also discuss the case when the quantum field has a nontrivial vacuum configuration.
Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be efficiently computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of the Dirichlet geometries. For the planar case a finite universal force is automatically found. Consistent with other calculations of the effect, for curved geometries divergent (non-universal) expressions are encountered. They are interpreted geometrically following Candelas …
The Casimir-Lifshitz formula for rectangular dielectric waveguide
本文分析了由两种不同介电材料组成的矩形波导中的Casimir-Lifshitz效应，采用表面模式技术推导出广义Lifshitz公式，实现了对Casimir-Lifshitz能量的精确计算，并在渐近极限下恢复了完美反射边界的经典表达式。
We evaluate the correlators for the vector potential and for the field strength tensor of the electromagnetic field in the geometry of two parallel planar plates in AdS spacetime. Two types of boundary conditions are considered on the plates. The first one is a generalization of perfect conductor boundary condition and the second one corresponds to the confining boundary conditions. By using the expressions for the correlators, the vacuum expectation values (VEVs) of the photon condensate and of the electric and magnetic fields squared are investigated. As another important local characteristi…
Casimir Forces in CFT with Defects and Boundaries
本文以局域相关双迹算符建模 CFT 的非理想缺陷与边界，计算多种点状、平板和平行膜构型间的量子 Casimir 力，并揭示其 UV/IR 行为、吸引性及普适压强标度。
We study the Casimir energy of a scalar field for a regular polygon with N sides. The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon. The polygon eigenvalues $λ_N$ are expressed in terms of the Dirichlet circle eigenvalues $λ_C$ as an expansion in $\frac{1}{N}$ of the form, $λ_N = λ_C (1 + \frac{4ζ(2)}{N^2} + \frac{4ζ(3)}{N^3} + \frac{28ζ(4)}{N^4}+...)$. A comparison follows between the Casimir energy on the polygon with N=4 found with our method and the Casimir energy of the scalar field on a square. We generalize the result to spaces of the form $R^d\times P…
We consider a quantum massless fermionic field in (1+1) dimensions in the case of moving boundaries. We work in the canonical approach in order to find a Hamiltonian describing the dynamics of the field. Thus, we study the statistics of work and particles produced from the vacuum by a linear driving of a boundary.
We calculate the Casimir interaction energy in $d=2$ spatial dimensions between two (zero-width) mirrors, one flat, and the other slightly curved, upon which {\em imperfect\/} conductor boundary conditions are imposed for an Electromagnetic (EM) field. Our main result is a second-order Derivative Expansion (DE) approximation for the Casimir energy, which is studied in different interesting limits. In particular, we focus on the emergence of a non-analyticity beyond the leading-order term in the DE, when approaching the limit of perfectly-conducting mirrors. We also show that the system conside…
The effect of edges and apertures on the Casimir energy of an arrangement of plates and boundaries can be calculated in terms of an effective nonlocal lower-dimensional field theory that lives on the boundary. This formalism has been developed in a number of previous papers and applied to specific examples with Dirichlet boundary conditions. Here we generalize the formalism to arbitrary boundary conditions. As a specific example, the geometry of a flat plate and a half-plate placed parallel to it is considered for a number of different boundary conditions and the area-dependent and edge depend…
We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the ``relative Casimir energy", which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a …
Fermionic dynamical Casimir effect: Magnus expansion
针对1+1维有质量狄拉克场在振荡全反射边界下的真空粒子对产生问题，采用S矩阵的马格努斯展开计算跃迁振幅，得到单对、多对产生振幅及单对振幅修正，并推导出入出福克空间玻戈留波夫变换的近似幺正表达式。
One of the most efficient methods for the evaluation of the vacuum expectation values for physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This enables to derive the renormalized quantities in a manifestly cutoff independent way and to present them in the form of strongly convergent integrals. However, applications of the Abel-Plana formula, in its usual form, are restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers. The author generalized the Abel-Plana formula which essentially enlarges its application r…
The Casimir effect giving rise to an attractive force between the configuration boundaries that confine the massless scalar field is rigorously proven for odd dimensional hypercube with the Dirichlet boundary conditions and different spacetime dimensions D by the Epstein zeta function regularization.
In this paper we have considered the particle creation in the spatially closed Robertson-Walker space-time. We considered a real massive scalar field which conformally coupled to the Robertson-Walker background. With the dependence of the scale factor on time, the case under consideration is a dynamical Casimir effect with moving boundaries.
Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform for studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this pape…
We propose a generalization of the superconducting circuit simulation of the dynamical Casimir effect where we consider relativistically moving boundary conditions following different trajectories. We study the feasibility of the setup used in the past to simulate the dynamical Casimir effect to reproduce richer relativistic trajectories differing from purely sinusoidal ones. We show how different relativistic oscillatory trajectories of the boundaries of the same period and similar shape produce a rather different spectrum of particles characteristic of their respective motions.
The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situati…
The generation of photons in a three dimensional rectangular cavity with two moving boundaries is studied by using the Multiple Scale Analysis (MSA). It is shown that number of photons are enhanced for the cavity whose walls oscillate symmetrically with respect to the center of the cavity. The non-stationary Casimir effect is also discussed for the cavity which oscillates as a whole.
A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related zeta functions are central. Nontrivial results concerning these functions are given. While part of their application agrees with previous knowledge, new results like the zeta-regularized electromagnetic Casimir energy for a circular wire are included.
The Casimir forces on two parallel plates in conformally flat domain wall background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries.
The Casimir effect giving rise to an attractive or repulsive force between the configuration boundaries that confine the massless scalar field is reexamined for one to three-dimensional pistons in this paper. Especially, we consider Casimir pistons with hybrid boundary conditions, where the boundary condition on the piston is Neumann and those on other surfaces are Dirichlet. We show that the Casimir force on the piston is always repulsive, in contrast with the same problem where the boundary conditions are Dirichlet on all surfaces.
The Casimir effect, reflecting quantum vacuum fluctuations in the electromagnetic field in a region with material boundaries, has been studied both theoretically and experimentally since 1948. The forces between dielectric and metallic surfaces both plane and curved have been measured at the 10 to 1 percent level in a variety of room-temperature experiments, and remarkable agreement with the zero-temperature theory has been achieved. In fitting the data various corrections due to surface roughness, patch potentials, curvature, and temperature have been incorporated. It is the latter that is th…
Dynamical Casimir effect for fermions in 2+1 dimensions
本文研究2+1维Dirac场在随时间变化的曲线边界条件下的费米子对产生现象，证明bag边界条件使效应最大化，并通过有效作用量和形变展开将首个非平凡贡献与静态边界的电磁真空极化张量联系起来。
We study non-superposition effects in the Dirichlet Casimir interaction energy for N boundaries in d spatial dimensions, quantifying its departure from the case of an interaction where a superposition principle is valid. We first derive some general results about those effects, and then show that they only become negligible when the distances between surfaces are larger than the sizes of each individual surface. We consider different examples in one, two and three spatial dimensions.
We review recent developments in the Casimir effect which arises in quantization volumes restricted by material boundaries and in spaces with non-Euclidean topology. The starting point of our discussion is the novel exact solution for the electromagnetic Casimir force in the configuration of a cylinder above a plate. The related work for the scalar Casimir effect in sphere-plate configuration is also considered, and the application region of the proximity force theorem is discussed. Next we consider new experiments on the measurement of the Casimir force between metals and between metal and se…
The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates. We also discuss mass scale shifts in such systems and their possible dynamical and geometrical nature.
The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.
In this work the Casimir effect is studied for scalar fields in the presence of boundaries and under the influence of arbitrary smooth potentials of compact support. In this setting, piston configurations are analyzed in which the piston is modeled by a potential. For these configurations, analytic results for the Casimir energy and force are obtained by employing the zeta function regularization method. Also, explicit numerical results for the Casimir force are provided for pistons modeled by a class of compactly supported potentials that are realizable as delta-sequences. These results are t…
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