arXiv subjects

Luiz A. Manzoni

Publications and source records attributed to Luiz A. Manzoni.

8 recordsLinked to original sources

arXiv2026

Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions

We consider the one-dimensional Dirac equation with the most general relativistic contact interaction supported on two points symmetrically located with respect to the origin. In order to determine the shape of the interaction, we use a distributional method, which in the present case is equivalent to the standard method of defining contact interactions by self-adjoint extensions of symmetric operators. The interaction on each of these two points depends on four parameters, each one having a clear physical meaning. We are interested in the scattering and confining properties of this model. We focus our attention on even or odd interactions under parity transformations and investigate the existence of critical and supercritical states, bound states, confinement and scattering resonances for some particular interactions of special interest.

quant-ph↗

arXiv2018

A probability distribution for quantum tunneling times

We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.

quant-ph↗

arXiv2014

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 Schrödinger 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 $δ^\prime$ interaction.

quant-ph↗

arXiv2013

Average clock times for scattering through asymmetric barriers

The reflection and transmission Salecker-Wigner-Peres clock times averaged over the post-selected reflected and transmitted sub-ensembles, respectively, are investigated for the one dimensional scattering of a localized wave packet through an asymmetric barrier. The dwell time averaged over the same post-selected sub-ensembles is also considered. The emergence of negative average reflection times is examined and we show that while the average over the reflected sub-ensemble eliminates the negative peaks at resonance for the clock time, it still allows negative values for transparent barriers. The saturation of the average times with the barrier width (Hartman effect) is also addressed.

quant-ph↗

arXiv2011

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).

quant-ph↗

arXiv2009

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.

quant-ph↗

arXiv2007

Relativistic Tunneling Through Two Successive Barriers

We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts, and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the Generalized Hartman Effect. We compare our results with the nonrelativistic ones and discuss their interpretation.

quant-ph↗

arXiv2002

A Theory of the Casimir Effect for Compact Regions

We develop a mathematically precise framework for the Casimir effect. Our working hypothesis, verified in the case of parallel plates, is that only the regularization-independent Ramanujan sum of a given asymptotic series contributes to the Casimir pressure. As an illustration, we treat two cases: parallel plates, identifying a previous cutoff free version (by G. Scharf and W. W.) as a special case, and the sphere.We finally discuss the open problem of the Casimir force for the cube. We propose an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive sign of the force.

hep-th↗