Influence of a magnetic fluxon on the vacuum energy of quantum fields confined by a bag

We study the simultaneous influence of boundary conditions and external fields on quantum fluctuations by considering vacuum zero-point energies for quantum fields in the presence of a magnetic fluxon confined by a bag, circular and spherical for bosons and circular for fermions. The Casimir effect is calculated in a generalized cut-off regularization after applying zeta-function techniques to eigenmode sums and using recent techniques about Bessel zeta functions at negative arguments

Complete zeta-function approach to the electromagnetic Casimir effect for spheres and circles

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.Comment: accepted in Ann. Phy

Conformal Sector in D=6D=6 Quantum Gravity

We discuss the conformal factor dynamics in $D=6$. Accepting the proposal that higher-derivative dimensionless terms in the anomaly-induced effective action may be dropped, we obtain a superrenormalizable (like in $D=4$) effective theory for the conformal factor. The one-loop analysis of this theory gives the anomalous scaling dimension for the conformal factor and provides a natural mechanism to solve the cosmological constant problem.Comment: 9 pages, Oct 27 199

Zeta-Regularization of the O(N) Non-Linear Sigma Model in D dimensions

The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M \times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$ correspond to flat space, a torus and a sphere, respectively. Using zeta regularization and the $1/N$ expansion, the corresponding partition functions and the gap equations are obtained. Numerical solutions of the gap equations at the critical coupling constants are given, for several values of $D$. The properties of the partition function and its asymptotic behaviour for large $D$ are discussed. In a similar way, a higher-derivative non-linear sigma model is investigated too. The physical relevance of our results is discussed.Comment: 26 page

Information content in Gaussian noise: optimal compression rates

We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized stochastic Gaussian signal (noise). The compression ratio decreases logarithmically with the amplitude of the frequency spectrum $P(f)$ of the noise. Entropy values and compression rates are shown to depend on the shape of this power spectrum, given different normalizations. The cases of white noise (w.n.), $f^{n_p}$ power-law noise ---including $1/f$ noise---, (w.n.$+1/f$) noise, and piecewise (w.n.+$1/f |$ w.n.$+1/f^2$) noise are discussed, while quantitative behaviours and useful approximations are provided.Comment: 28 LateX pages and 6 Fig, replaced with minor changes to match published versio

Coding depth perception from image defocus

AbstractAs a result of the spider experiments in Nagata et al. (2012), it was hypothesized that the depth perception mechanisms of these animals should be based on how much images are defocused. In the present paper, assuming that relative chromatic aberrations or blur radii values are known, we develop a formulation relating the values of these cues to the actual depth distance. Taking into account the form of the resulting signals, we propose the use of latency coding from a spiking neuron obeying Izhikevich’s ‘simple model’. If spider jumps can be viewed as approximately parabolic, some estimates allow for a sensory-motor relation between the time to the first spike and the magnitude of the initial velocity of the jump

Regularized Casimir energy for an infinite dielectric cylinder subject to light-velocity conservation

The Casimir energy of a dilute dielectric cylinder, with the same light-velocity as in its surrounding medium, is evaluated exactly to first order in $\xi^2$ and numerically to higher orders in $\xi^2$. The first part is carried out using addition formulas for Bessel functions, and no Debye expansions are required