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

Statistical evaluation of the flux cross-calibration of the XMM-Newton EPIC cameras

The second XMM-Newton serendipitous source catalogue, 2XMM, provides the ideal data base for performing a statistical evaluation of the flux cross-calibration of the XMM-Newton European Photon Imaging Cameras (EPIC). We aim to evaluate the status of the relative flux calibration of the EPIC cameras on board XMM-Newton (MOS1, MOS2, and pn) and investigate the dependence of the calibration on energy, position in the field of view of the X-ray detectors, and lifetime of the mission. We compiled the distribution of flux percentage differences for large samples of 'good quality' objects detected with at least two of the EPIC cameras. The mean offset of the fluxes and dispersion of the distributions was then found by Gaussian fitting. Count rate to flux conversion was performed with a fixed spectral model. The impact on the results of varying this model was investigated. Excellent agreement was found between the two EPIC MOS cameras to better than 4% from 0.2 keV to 12.0 keV. MOS cameras register 7-9% higher flux than pn below 4.5 keV and 10-13% flux excess above 4.5 keV. No evolution of the flux ratios is seen with time, except at energies below 0.5 keV, where we found a strong decrease in the MOS to pn flux ratio with time. This effect is known to be due to a gradually degrading MOS redistribution function. The flux ratios show some dependence on distance from the optical axis in the sense that the MOS to pn flux excess increases with off-axis angle. Furthermore, in the 4.5-12.0 keV band there is a strong dependence of the MOS to pn excess flux on the azimuthal-angle. These results strongly suggest that the calibration of the Reflection Grating Array (RGA) blocking factors is incorrect at high energies. Finally, we recommend ways to improve the calculation of fluxes in future versions of XMM-Newton source catalogues.Comment: 11 pages, 10 figures, 3 tables. Abridged Abstract. Accepted for publication in Astronomy and Astrophysic

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

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

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