Distributional approach to point interactions in one-dimensional quantum mechanics

We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schr\"odinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $\delta^\prime$ interaction.Comment: Open Access link: http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstrac

Salecker-Wigner-Peres clock and average tunneling times

The quantum clock of Salecker-Wigner-Peres is used, by performing a post-selection of the final state, to obtain average transmission and reflection times associated to the scattering of localized wave packets by static potentials in one dimension. The behavior of these average times is studied for a gaussian wave packet, centered around a tunneling wave number, incident on a rectangular barrier and, in particular, on a double delta barrier potential. The regime of opaque barriers is investigated and the results show that the average transmission time does not saturate, showing no evidence of the Hartman effect (or its generalized version).Comment: 9 pages, 4 figure

The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

On the Salecker-Wigner-Peres clock and double barrier tunneling

In this work we revisit the Salecker-Wigner-Peres clock formalism and show that it can be directly applied to the phenomenon of tunneling. Then we apply this formalism to the determination of the tunneling time of a non relativistic wavepacket, sharply concentrated around a tunneling energy, incident on a symmetric double barrier potential. In order to deepen the discussion about the generalized Hartmann effect, we consider the case in which the clock runs only when the particle can be found inside the region \emph{between} the barriers and show that, whenever the probability to find the particle in this region is non negligible, the corresponding time (which in this case turns out to be a dwell time) increases with the barrier spacing.Comment: To appear in Phys. Rev.

Torsion and the Gravitational Interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The coupling prescription implied by this principle is found to be always equivalent with that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.Comment: Version 2: minor presentation changes, a reference added, 11 pages (IOP style

Experimental evaluation of the usage of ad hoc networks as stubs for multiservice networks

This paper describes an experimental evaluation of a multiservice ad hoc network, aimed to be interconnected with an infrastructure, operator-managed network. This network supports the efficient delivery of services, unicast and multicast, legacy and multimedia, to users connected in the ad hoc network. It contains the following functionalities: routing and delivery of unicast and multicast services; distributed QoS mechanisms to support service differentiation and resource control responsive to node mobility; security, charging, and rewarding mechanisms to ensure the correct behaviour of the users in the ad hoc network. This paper experimentally evaluates the performance of multiple mechanisms, and the influence and performance penalty introduced in the network, with the incremental inclusion of new functionalities. The performance results obtained in the different real scenarios may question the real usage of ad-hoc networks for more than a minimal number of hops with such a large number of functionalities deployed