δ−δ′\delta-\delta^\prime generalized Robin boundary conditions and quantum vacuum fluctuations

The effects induced by the quantum vacuum fluctuations of one massless real scalar field on a configuration of two partially transparent plates are investigated. The physical properties of the infinitely thin plates are simulated by means of Dirac-$\delta-\delta^\prime$ point interactions. It is shown that the distortion caused on the fluctuations by this external background gives rise to a generalization of Robin boundary conditions. The $T$-operator for potentials concentrated on points with non defined parity is computed with total generality. The quantum vacuum interaction energy between the two plates is computed using the $TGTG$ formula to find positive, negative, and zero Casimir energies. The parity properties of the $\delta-\delta^\prime$ potential allow repulsive quantum vacuum force between identical plates.Comment: 21 pages and 11 figures. PhysRev

Quantum scalar fields in the half-line. A heat kernel/zeta function approach

In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated in terms of Riemann Theta functions, the error function, and hypergeometric PFQ functions.Comment: Latex file, 11 pages, 7 figure

Two-point one-dimensional δ\delta-δ′\delta^\prime interactions: non-abelian addition law and decoupling limit

In this contribution to the study of one dimensional point potentials, we prove that if we take the limit $q\to 0$ on a potential of the type $v_0\delta({y})+{2}v_1\delta'({y})+w_0\delta({y}-q)+ {2} w_1\delta'({y}-q)$, we obtain a new point potential of the type ${u_0} \delta({y})+{2 u_1} \delta'({y})$, when $u_0$ and $u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({\mathbb R})$. We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the exceptional cases emerging in the study are also described in full detail. It is shown that for the $v_1=\pm 1$, $w_1=\pm 1$ values of the $\delta^\prime$ couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side

Survival and Nonescape Probabilities for Resonant and Nonresonant Decay

In this paper we study the time evolution of the decay process for a particle confined initially in a finite region of space, extending our analysis given recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly the time-dependent Schroedinger equation for a finite-range potential. We calculate and compare two quantities: (i) the survival probability S(t), i.e., the probability that the particle is in the initial state after a time t; and (ii) the nonescape probability P(t), i.e., the probability that the particle remains confined inside the potential region after a time t. We analyze in detail the resonant and nonresonant decay. In the former case, after a very short time, S(t) and P(t) decay exponentially, but for very long times they decay as a power law, albeit with different exponents. For the nonresonant case we obtain that both quantities differ initially. However, independently of the resonant and nonresonant character of the initial state we always find a transition to the ground state of the system which indicates a process of ``loss of memory'' in the decay.Comment: 26 pages, RevTex file, figures available upon request from [email protected] (To be published in Annals of Physics

X-ray sources as tracers of the large-scale structure in the Universe

We review the current status of studies of large-scale structure in the X-ray Universe. After motivating the use X-rays for cosmological purposes, we discuss the various approaches used on different angular scales including X-ray background multipoles, cross-correlations of the X-ray background with galaxy catalogues, clustering of X-ray selected sources and small-scale fluctuations and anisotropies in the X-ray background. We discuss the implications of the above studies for the bias parameter of X-ray sources, which is likely to be moderate for X-ray selected AGN and the X-ray background (~1-2). We finally outline how all-sky X-ray maps at hard X-rays and medium surveys with large sky coverage could provide important tests for the cosmological models.Comment: Invited review presented at the Workshop X-ray Astronomy'99: Stellar endpoints, AGN and the diffuse X-ray background (Astrophys Lett and Comm