Attractive and repulsive Casimir vacuum energy with general boundary conditions

The infrared behaviour of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth–Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.     

Vacuum Boundary Effects

The Casimir effect is highly dependent on the shape and structure of space boundaries. This dependence is encoded in the variation of vacuum energy with the different types of boundary conditions. We analyze from a global perspective the properties of the Casimir energy as a function on the largest space of the consistent boundary conditions M_F\mathcal{M}_{F} for a massless scalar field confined between to homogeneous parallel plates. In particular, we analyze the analytic properties of this function and point out the existence of a third order phase transition at periodic boundary conditions. We also characterize the boundary conditions which give rise to attractive or repulsive Casimir forces. In the interface between both regimes we find a very interesting family of boundary conditions without Casimir effect, and fully characterize the boundary conditions which do not induce any type of Casimir force.     

Radiative corrections to the Casimir pressure under the influence of temperature and external fields

Generalizing the quantum field theory (QFT) with boundary conditions in covariant gauge to the case of finite temperature, we develop the quantum electrodynamics (QED) with boundary conditions in the Matsubara approach as well as in the thermofield formulation. We rederive the known results of the free-field theory for the pressure and the free energy of the Casimir problem. For infinitely thin plates we calculate the radiative corrections in secondorder perturbation theory at finite temperature. Thereby it turns out that the calculation of the vacuum energy at the vanishing temperature via the Z functional is much simpler than a calculation via the energy momentum tensor. This observation allows determination of the influence of static electromagnetic fields on the Casimir problem.     

Casimir Effect in Hemisphere Capped Tubes

In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2 + 1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.     

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.     

The Casimir effect for fermions in one dimension

We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a “Dirac spike”) and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes.     

Weak Gravitational Field and Casimir Energy

In this paper we consider the effect of a weak gravitation field on the Casimir energy. Under a weak perturbation of a metric, we first obtain the linear energy-momentum tensor of a scalar field in a generic background and then the corrected energy of a scalar filed which satisfies the Dirichlet boundary condition is calculated up to first order of the metric perturbation. We show that our results coincide to the previous related works e.g., the Casimir effect when studied in Fermi coordinates.     

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.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

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.     

SUSY QM in a One-Dimensional Box and Local Observable Quantities

We investigate several Hamiltonians for a free particle in a one-dimensional box, in the context of supersymmetric quantum mechanics. Specifically, we study this problem with the Neumann boundary condition, the periodic and antiperiodic boundary condition, and some mixed and complex boundary conditions. This is achieved by using an approach recently proposed which expresses the factorization of the partner Hamiltonians in terms of the probability density and current for the ground-state eigenfunction of one of them.     

卡西米尔力

量子电动力学中的卡西米尔力是真空零点能的体现.广义的卡西米尔力则依赖于涨落介质的类型广泛地出现于物理中,包括量子,临界,戈德斯通模,以及非平衡卡西米尔力.长程关联的涨落介质和约束是产生卡西米尔力的两个条件.本文通过回顾卡西米尔物理的发展,讨论了不同类型的卡西米尔力,几种正规化方法,并对卡西米尔物理的进一步发展做了展望.     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.     

Casimir Effect for Two Parallel Plates Through a Gupta-Bleuler Type Quantization on the Static Domain Wall Background

In this paper, Casimir energy-momentum tensor for a conformally coupled scalar field in the presence of two parallel plates with Dirichlet boundary condition on background of planar domain wall is investigated. We show that by utilizing a Gupta-Bleuler type quantization approach, one can obtain finite result for the vacuum expectation values of the energy-momentum tensor. In addition, we calculate the pressures on the plates and energy density between two plates and show that they satisfy the standard thermodynamical relations.     

Casimir Force of Piston Systems with Arbitrary Cross Sections under Different Boundary Conditions

We study the Casimir force between two pistons under different boundary conditions inside an infinite cylinder with arbitrary cross section. It is found that the attractive or repulsive character of the Casimir force for a scalar field is determined only by the boundary condition along the longitudinal direction and is independent of the cross section, transverse boundary conditions and the mass of the field. Under symmetric Dirichlet-Dirichlet, Neumann-Neumann and periodic longitudinal boundary conditions the Casimir force is always attractive, but is repulsive under non-symmetric Dirichlet-Neumann and anti-periodic longitudinal boundary conditions. The Casimir force of the electromagnetic field in an ideal conductive piston is also investigated. This force is always attractive regardless of the shape of the cross section and the transverse boundary conditions.     

Quantum vacuum fluctuations

The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences, like the Casimir effect, which is now measured with good accuracy and agreement with theory, provided that the latter accounts for differences between real experiments and the ideal situation considered by Casimir. But the vacuum energy density calculated by adding field mode energies is much larger than the density observed around us through gravitational phenomena. This ‘vacuum catastrophe’ is one of the unsolved problems at the interface between quantum theory on one hand, inertial and gravitational phenomena on the other hand. It is however possible to put properly formulated questions in the vicinity of this paradox. These questions are directly connected to observable effects bearing upon the principle of relativity of motion in quantum vacuum.     

柱环腔中的量子电动力学效应

研究以同轴不同半径柱面围成的导体柱环腔体中电磁场真空零点振动模式所给出的宏观量子效应.零点振动模式通过求解柱环空腔边界条件下无源的Maxwell方程组获得.得到了双柱面同心柱环中单位长度和单位面积的且是有限的真空能量，即Casimir能量.这有限的Casimir能量可以分解为独立而且收敛的三部分，它们分别来自内柱面、外柱面和柱环之中.对多柱面同心柱环，Casimir能量可分解为独立的（2n—1）部分（n为柱面数）.柱环是类似于平行板的几何结构.但柱环所给出的Casimir能量和Casimir势能系数是随着 关键词： Casimir效应 柱环腔体 零点能 量子电动力学     

Interface energies in ising spin glasses

The replica method has been used to calculate the interface free energy associated with the change from periodic to antiperiodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes, but after allowing for fluctuation effects, a nonzero interface free energy is obtained which is significantly different from numerical expectations.     

Dynamics of quantum Fisher information in a two-level system coupled to multiple bosonic reservoirs

We consider the optimal parameter estimation for a two-level system coupled to multiple bosonic reservoirs. By using quantum Fisher information(QFI), we investigate the effect of the Markovian reservoirs' number N on QFI in both weak and strong coupling regimes for a two-level system surrounded by N zero-temperature reservoirs of field modes initially in the vacua. The results show that the dynamics of QFI non-monotonically decays to zero with revival oscillations at some time in the weak coupling regime depending on the reservoirs' parameters. Furthermore, we also present the relations between the QFI flow, the flows of energy and information, and the sign of the decay rate to gain insight into the physical processes characterizing the dynamics.     

TheXY model and the three-state antiferromagnetic Potts model in three dimensions: Critical properties from fluctuating boundary conditions

We present the results of a Monte Carlo study of the three-dimensionalXY model and the three-dimensional antiferromagnetic three-state Potts model. In both cases we compute the difference of the free energies of a system with periodic and a system with antiperiodic boundary conditions in a neighborhood of the critical coupling. From the finite-size scaling behaviour of this quantity we extract values for the critical temperature and the critical exponentv that are compatible with recent high-statistics Monte Carlo studies of the models. The results for the free energy difference at the critical temperature and for the exponentv confirm that both models belong to the same universality class.