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Pietro Rotelli

Publications and source records attributed to Pietro Rotelli.

At least 19 recordsLinked to original sources
arXiv2013

Antiparticle creation in tunneling

We study particle interaction with a Dirac step potential. In the standard Klein energy zone, the hypothesis of Klein pair production predicts the existence of free/oscillatory antiparticles. In this paper, we discuss the tunneling energy zone characterized by evanescent wave functions in the classically forbidden region. We ask the question of the nature, particle or antiparticle, of the densities within the classically forbidden region. The answer to this question is relevant to the correct form of the reflection coefficient.

quant-ph↗
arXiv2012

Relative helicity phases in planar Dirac scattering

We study planar Dirac scattering for an electrostatic stratified barrier potential. The general expressions for transmitted and reflected waves are derived. Of particular interest is the information upon relative helicity phases. We also briefly discuss some possible applications.

quant-ph↗
arXiv2012

Graphene tests of Klein phenomena

Graphene is characterized by chiral electronic excitations. As such it provides a perfect testing ground for the production of Klein pairs (electron/holes). If confirmed, the standard results for barrier phenomena must be reconsidered with, as a byproduct, the accumulation within the barrier of holes.

quant-ph↗
arXiv2012

Resonant laser tunnelling

We propose an experiment involving a gaussian laser tunneling through a twin barrier dielectric structure. Of particular interest are the conditions upon the incident angle for resonance to occur. We provide some numerical calculations for a particular choice of laser wave length and dielectric refractive index which confirm our expectations.

physics.optics↗
arXiv2011

Wave and Particle Limit for Multiple Barrier Tunneling

The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the plane wave results. In particular, the existence of resonance/transparency for twin tunnelling in the wave limit is immediately obvious. The known resonances for three and four barriers are also derived. The transition from the wave limit to the particle limit is exhibit numerically.

quant-ph↗
arXiv2011

Laser Interaction with a Dielectric Block

Some optical experiments provide the easiest way to test quantum mechanical predictions. Such a situation applies to a laser beam traversing a dielectric structure. The dielectric structure mir- roring quantum mechanical potentials. The simplest of these, studied in this paper, involves a single dielectric block. We exhibit both by analytic and numerical calculations explicit examples of total coherence and total incoherence phenomena. Which case appears depends upon the angle of incidence of the laser beam and/or the dimensions of beam vs block width. Unlike our previ- ous studies our calculations here are three-dimensional, although, with suitable approximations, somewhat simpler planar expressions can be derived.

physics.optics↗
arXiv2010

Planar Dirac diffusion

We present the results of the planar diffusion of a Dirac particle by step and barrier potentials, when the incoming wave impinges at an arbitrary angle with the potential. Except for right-angle incidence this process is characterized by the appearance of spin flip terms. For the step potential, spin flip occurs for both transmitted and reflected waves. However, we find no spin flip in the transmitted barrier result. This is surprising because the barrier result may be derived directly from a two-step calculation. We demonstrate that the spin flip cancellation indeed occurs for each particle (wave packet) contribution.

hep-th↗
arXiv2009

Localized Beams and Dielectric Barriers

Recalling the similarities between the Maxwell equations for a transverse electric wave in a stratified medium and the quantum mechanical Schroedinger equation in a piece-wise potential, we investigate the analog of the so called particle limit in quantum mechanics. It is shown that in this limit the resonance phenomena are lost since individual reflection and transmission terms no longer overlap. The result is a stationary zebra-like response with the intensity in each stripe calculable.

quant-ph↗
arXiv2008

Fermion-Fermion Bound State Condition for Scalar Exchanges

The condition for the existence of a bound state between two fermions exchanging massive scalars is derived. For low scalar mass, we reproduce the scalar field model result. The high scalar mass result exhibits a somewhat different inequality condition.

hep-th↗
arXiv2008

Bound State Inequality for High Mass Exchanges in a Scalar Field Model

Ladder diagrams are relevant for the study of bound states. The condition upon the coupling strength for the existence of a bound state has been deduced in a scalar field theory for the case of low mass exchanges. We apply this approach to the case of very high mass exchanges.

hep-th↗
arXiv2006

Barrier Paradox in the Klein Zone

We study the solutions for a one-dimensional electrostatic potential in the Dirac equation when the incoming wave packet exhibits the Klein paradox (pair production). With a barrier potential we demonstrate the existence of multiple reflections (and transmissions). The antiparticle solutions which are necessarily localized within the barrier region create new pairs with each reflection at the potential walls. Consequently we encounter a new paradox for the barrier because successive outgoing wave amplitudes grow geometrically.

hep-th↗
arXiv2006

Above Barrier Dirac Multiple Scattering and Resonances

We extend an above barrier analysis made with the Schrodinger equation to the Dirac equation. We demonstrate the perfect agreement between the barrier results and back to back steps. This implies the existence of multiple (indeed infinite) reflected and transmitted wave packets. These packets may be well separated in space or partially overlap. In the latter case interference effects can occur. For the extreme case of total overlap we encounter resonances. The conditions under which resonance phenomena can be observed is discussed and illustrated by numerical calculations.

hep-th↗
arXiv2004

Tunnelling Through Two Barriers

Recent studies of the tunnelling through two opaque barriers claim that the transit time is independent of the barrier widths and of the separation distance between the barriers. We observe, in contrast, that if multiple reflections are allowed for correctly (infinite peaks) the transit time between the barriers appears exactly as expected.

quant-ph↗
arXiv2001

Remarks upon the mass oscillation formulas

The standard formula for mass oscillations is often based upon the approximation $t \approx L$ and the hypotheses that neutrinos have been produced with a definite momentum $p$ or, alternatively, with definite energy $E$. This represents an inconsistent scenario and gives an unjustified reduction by a factor of two in the mass oscillation formulas. Such an ambiguity has been a matter of speculations and mistakes in discussing flavour oscillations. We present a series of results and show how the problem of the factor two in the oscillation length is not a consequence of gedanken experiments, i.e. oscillations in time. The common velocity scenario yields the maximum simplicity.

hep-ph↗
arXiv1997

Local Hypercomplex Analyticity

The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of hypercomplex solutions. The result is the definition of a generalized complex analyticity to hypercomplex space. 02.10.Tq/Vr, 02.30.-f/Dk, 02.90.+p

funct-an↗
arXiv1996

Quaternionic Electroweak Theory

We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar solutions are also discussed.

hep-th↗
arXiv1996

Odd Dimensional Translation between Complex and Quaternionic Mechanics

We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with a complex geometry. In particular we describe how to reduce ($2n$+$1$)-dimensional complex matrices to {\em overlapping\/} ($n$+$1$)-dimensional quaternionic matrices with generalized quaternionic elements. This step resolves an outstanding difficulty with reduction of purely complex matrix groups within quaternionic QM and avoids {\em anomalous} eigenstates. As a result we present a more complete translation from CQM to QQM and viceversa.

hep-th↗