Vacuum energy of a massive scalar field in the presence of a semi-transparent cylinder

We compute the ground state energy of a massive scalar field in the background of a cylindrical shell whose potential is given by a delta function. The zero point energy is expressed in terms of the Jost function of the related scattering problem, the renormalization is performed with the help of the heat kernel expansion. The energy is found to be negative for attractive and for repulsive backgrounds as well.Comment: 17 pages, 5 figure

Casimir effect in a wormhole spacetime

We consider the Casimir effect for quantized massive scalar field with non-conformal coupling $\xi$ in a spacetime of wormhole whose throat is rounded by a spherical shell. In the framework of zeta-regularization approach we calculate a zero point energy of scalar field. We found that depending on values of coupling $\xi$, a mass of field $m$, and/or the throat's radius $a$ the Casimir force may be both attractive and repulsive, and even equals to zero.Comment: 2 figures, 10 pages, added 2 reference

Taming Model Uncertainty in Self-adaptive Systems Using Bayesian Model Averaging

Research on uncertainty quantification and mitigation of software-intensive systems and (self-)adaptive systems, is increasingly gaining momentum, especially with the availability of statistical inference techniques (such as Bayesian reasoning) that make it possible to mitigate uncertain (quality) attributes of the system under scrutiny often encoded in the system model in terms of model parameters. However, to the best of our knowledge, the uncertainty about the choice of a specific system model did not receive the deserved attention.This paper focuses on self-adaptive systems and investigates how to mitigate the uncertainty related to the model selection process, that is, whenever one model is chosen over plausible alternative and competing models to represent the understanding of a system and make predictions about future observations. In particular, we propose to enhance the classical feedback loop of a self-adaptive system with the ability to tame the model uncertainty using Bayesian Model Averaging. This method improves the predictions made by the analyze component as well as the plan that adopts metaheuristic optimizing search to guide the adaptation decisions. Our empirical evaluation demonstrates the cost-effectiveness of our approach using an exemplar case study in the robotics domain

Local and Global Casimir Energies for a Semitransparent Cylindrical Shell

The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a $\lambda\delta$-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined for both weak and strong coupling, the latter being the well-studied Dirichlet cylinder case. For weak-coupling,through $\mathcal{O}(\lambda^2)$, the total energy is shown to vanish by both analytic and numerical arguments, based both on Green's-function and zeta-function techniques. Divergences occurring in the calculation are shown to be absorbable by renormalization of physical parameters of the model. The global energy may be obtained by integrating the local energy density only when the latter is supplemented by an energy term residing precisely on the surface of the cylinder. The latter is identified as the integrated local energy density of the cylindrical shell when the latter is physically expanded to have finite thickness. Inside and outside the delta-function shell, the local energy density diverges as the surface of the shell is approached; the divergence is weakest when the conformal stress tensor is used to define the energy density. A real global divergence first occurs in $\mathcal{O}(\lambda^3)$, as anticipated, but the proof is supplied here for the first time; this divergence is entirely associated with the surface energy, and does {\em not} reflect divergences in the local energy density as the surface is approached.Comment: 28 pages, REVTeX, no figures. Appendix added on perturbative divergence

Vacuum energy in the presence of a magnetic string with delta function profile

We present a calculation of the ground state energy of massive spinor fields and massive scalar fields in the background of an inhomogeneous magnetic string with potential given by a delta function. The zeta functional regularization is used and the lowest heat kernel coefficients are calculated. The rest of the analytical calculation adopts the Jost function formalism. In the numerical part of the work the renormalized vacuum energy as a function of the radius $R$ of the string is calculated and plotted for various values of the strength of the potential. The sign of the energy is found to change with the radius. For both scalar and spinor fields the renormalized energy shows no logarithmic behaviour in the limit $R\to 0$, as was expected from the vanishing of the heat kernel coefficient $A_2$, which is not zero for other types of profiles.Comment: 30 pages, 10 figure

The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

We calculate the zero point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta function type. We use zeta functional regularization and express the regularized ground state energy in terms of the Jost function of the related scattering problem. Then we find the corresponding heat kernel coefficients and perform the renormalization, imposing the normalization condition that the ground state energy vanishes when the mass of the quantum field becomes large. Finally the ground state energy is calculated numerically. Corresponding plots are given for different values of the strength of the background potential, for both attractive and repulsive potentials.Comment: 15 pages, 5 figure

Heat Kernel Expansion for Semitransparent Boundaries

We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel coefficients.Comment: 16 page