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Erasmo Recami

Publications and source records attributed to Erasmo Recami.

At least 55 records · Page 3Linked to original sources
arXiv2007

Deriving Spin within a discrete-time theory

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called "Non-Newtonian Mechanics"). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.'s formulation).

quant-ph↗
arXiv2005

Multi-verses, Micro-universes and Elementary Particles (Hadrons)

We present here a panoramic view of our unified, bi-scale theory of gravitational and strong interactions [which is mathematically analogous to the last version of N.Rosen's bi-metric theory, and yields physical results similar to strong gravity's]. This theory, developed during the last 25 years, is purely geometrical in nature, adopting the methods of general relativity for the description of hadron structure and strong interactions. In particular, hadrons can be associated with "strong black-holes", from the external point of view, and with micro-universes, from the internal point of view. Among the results presented in this extended summary, let us mention the elementary derivation: (i) of confinement and (ii) asymptotic freedom for the hadron constituents; (iii) of the Yukawa behaviour for the strong potential at the static limit; (iv) of the strong coupling "constant", and (v) of mesonic mass spectra. Incidentally, within the present approach, results obtained for hadrons can yield information about the corresponding multi-verses, and viceversa.

physics.gen-ph↗
arXiv2004

Resonant and non-resonant Tunneling through a double barrier

An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the behavior of the transmission coefficient and of the tunneling phase-time near a resonance is given by expressions with "Breit-Wigner type" denominators. By contrast, it is shown that, when the tunneling probability is low (but not negligible), the non-resonant tunneling time depends on the barrier width and on the distance between the barriers only in a very weak (exponentially decreasing) way: This can imply in various cases, as well-known, the highly Superluminal tunneling associated with the so-called "generalized Hartman Effect"; but we are now able to improve and modify the mathematical description of such an effect, and to compare more in detail our results with the experimental data for non-resonant tunneling of photons. Finally, as a second example, the tunneling phase-time is calculated, and compared with the available experimental results, in the case of the quantum-mechanical tunneling of neutrons through two barrier-filters at the resonance energy of the set-up.

quant-ph↗
arXiv2004

Chirped optical X-shaped pulses in material media

In this paper we analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shape after some propagation distance, while the ordinary chirped gaussian-pulses can recover their longitudinal shape only (since gaussian pulses suffer a progressive spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during the pulse propagation.

physics.optics↗
arXiv2003

Focused X-shaped (Superluminal) pulses

The space-time focusing of a (continuous) succession of localized X-shaped pulses is obtained by suitably integrating over their speed, i.e., over their axicon angle, thus generalizing a previous (discrete) approach. First, new Superluminal wave pulses are constructed, and then tailored in such a wave to get them temporally focused at a chosen spatial point, where the wavefield can reach for a short time very high intensities. Results of this kind may find applications in many fields, besides electromagnetism and optics, including acoustics, gravitation, and elementary particle physics. PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az; 42.82.Et; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Localized solutions to Maxwell equations; Superluminal waves; Bessel beams; Limited-diffraction pulses; Finite-energy waves; Electromagnetic wavelets; X-shaped waves; Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic waves; Seismic waves; Mechanical waves; Elementary particle physics; Gravitational waves

physics.class-ph↗
arXiv2002

The X-shaped, localized field generated by a Superluminal electric charge

It is now wellknown that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group-velocities (0 < v_g < infinity). Some of them, which are rigidly moving and have been called localized solutions, attracted large attention. In particular, much work has been done with regard to the Superluminal localized solutions (SLS), the most interesting of which resulted to be the "X-shaped" ones. The SLSs have been actually produced in a number of experiments, always by suitable interference of ordinary-speed waves. In this note we show, by contrast, that even a Superluminal charge creates an electromagnetic X-shaped wave. Namely, on the basis of Maxwell equations, we are able to evaluate the field associated with a Superluminal charge (under the approximation of pointlikeness): and it results to constitute a very simple example of true X-wave. [PACS nos.: 03.50.De; 03.30.+p; 41.20;Jb; 04.30.Db. Keywords: Special relativity; Maxwell equations; Superluminal waves; X-shaped waves; Localized beams; Wave propagation; Superluminal charges].

physics.class-ph↗
arXiv2002

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies

By a generalized bidirectional decomposition method, we obtain many new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; various of them being endowed with finite total energy. We construct, among the others, an infinite family of generalizations of the so-called "X-shaped" waves. [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Bidirectional decomposition; Bessel beams; X-shaped waves; Microwaves; Optics; Special relativity; Acoustics; Seismology; Mechanical waves; Elastic waves; Gravitational waves; Elementary particle physics].

physics.gen-ph↗
arXiv2002

Superluminal X-shaped beams propagating without distortion along a coaxial guide

In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039], we showed that localized Superluminal solutions to the Maxwell equations exist, which propagate down (non-evanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous non-dispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, geophysics, etc.). [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Coaxial cables; Bidirectional decomposition; Bessel beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical waves; Elastic waves; Guided gravitational waves.]

physics.class-ph↗
arXiv2002

Superluminal Localized Solutions to the wave equation, in (vacuum or) dispersive media, for arbitrary frequencies and with adjustable bandwidth

In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.Vr ; 62.30.+d ; 43.60.+d ; 91.30.Fn ; 04.30.Nk ; 42.25.Bs ; 46.40.Cd ; 52.35.Lv. Keywords: Wave equation; Wave propagation; Optics; Localized beams; Superluminal waves; Bessel beams; X-shaped waves; Acoustics; Mechanical waves; Dispersion compensation; Seismology; Geophysics; Gravitational Waves; Elementary particle physics].

physics.class-ph↗
arXiv2002

Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case

In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell equations to exist, which propagate without distortion with Superluminal speed along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those solutions possessed therefore infinite energy. In this note we show how to obtain, by contrast, finite-energy solutions, with the same localization and Superluminality properties. [PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az; 42.82.Et. Keywords: Wave-guides; Localized solutions to Maxwell equations; Superluminal waves; Bessel beams; Limited-dispersion beams; Finite-energy waves; Electromagnetic wavelets; X-shaped waves; Evanescent waves; Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic waves; Seismic waves; Mechanical waves; Elastic waves; Guided gravitational waves.]

physics.class-ph↗
arXiv2002

A simple quantum equation for Decoherence and dissipation (through interaction with the environment)

Within the density matrix formalism, it is shown that a simple way to get decoherence is through the introduction of a "quantum" of time (chronon): which implies replacing the differential Liouville--von Neumann equation with a finite-difference version of it. In this way, one is given the possibility of using a rather simple quantum equation to describe the decoherence effects due to dissipation. Namely, the mere introduction (not of a "time-lattice", but simply) of a "chronon" allows us to go on from differential to finite-difference equations; and in particular to write down the quantum-theoretical equations (Schroedinger equation, Liouville--von Neumann equation,...) in three different ways: "retarded", "symmetrical", and "advanced". One of such three formulations --the retarded one-- describes in an elementary way a system which is exchanging (and losing) energy with the environment; and in its density-matrix version, indeed, it can be easily shown that all non-diagonal terms go to zero very rapidly. [A much larger presentation of the theoretical ground on which this paper is based appeared in the e-print quant-ph/9706059, and in the preprint IC/98/74, ICTP; Trieste, 1998].

quant-ph↗
arXiv2002

Spin and Electron Structure

The recent literature shows a renewed interest, with various independent approaches, in the classical models for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore their physical and mathematical meaning, by the natural and powerful language of Clifford algebras (which, incidentally, will allow us to unify those different approaches). In such models, the ordinary electron is in general associated to the mean motion of a point--like "constituent" Q, whose trajectory is a cylindrical helix. We find, in particular, that the object Q obeys a new, non-linear Dirac--like equation, such that --when averaging over an internal cycle (which corresponds to a linearization)-- it transforms into the ordinary Dirac equation (valid, of course, for the electron as a whole).

quant-ph↗
arXiv2002

Superluminal effects for quantum tunneling through two successive barriers

We study the phenomenon of one-dimensional non-resonant tunnelling through two successive potential barriers, separated by an intermediate free region R, by analyzing the relevant solutions to the Schroedinger equation. We find that the total traversal time is INDEPENDENT not only of the barrier widths (the so-called "Hartman effect"), but also of the R-width: so that the effective velocity in the region R, between the two barriers, can be regarded as infinite. This agrees with the results known from the corresponding waveguide experiments, which simulated the tunnelling experiment herein considered because of the formal identity between the Schroedinger and the Helmholtz equation [PACS numbers: 73.40.Gk; 03.65.-w; 03.30.+p; 41.20.Jb; 84.40.Az].

quant-ph↗
arXiv2001

The strong coupling constant

In this paper we fix our attention, on hadron structure, and show that also the strong interaction strength alpha_S, ordinarily called the "(perturbative) coupling--constant square}", can be evaluated within our theory, and found to decrease (increase) as the "distance" r decreases (increases). This yields both the confinement of the hadron constituents, and their asymptotic freedom: in qualitative agreement with the experimental evidence. In other terms, our approach leads us, on a purely theoretical ground, to a dependence of alpha_S on r which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this work.

physics.gen-ph↗
arXiv2001

Unified time analysis of photon and (nonrelativistic) particle Tunnelling, and the Superluminal group-velocity problem

A unified approach to the time analysis of tunnelling of nonrelativistic particles is presented, in which Time is regarded as a quantum-mechanical observable, canonically conjugated to Energy. The validity of the Hartman effect (independence of the Tunnelling Time of the opaque barrier width, with Superluminal group velocities as a consequence) is verified for ALL the known expressions of the mean tunnelling time. Moreover, the analogy between particle and photon tunnelling is suitably exploited. On the basis of such an analogy, an explanation of some recent microwave and optics experimental results on tunnelling times is proposed. Attention is devoted to some aspects of the causality problem for particle and photon tunnelling.

quant-ph↗
arXiv2001

Superluminal motions? A bird-eye view of the experimental situation

In this article (after some brief theoretical considerations) a bird-eye view is presented -with the help of nine figures- of the various experimental sectors of physics in which Superluminal motions seem to appear. In particular, a panorama is presented of the experiments with evanescent waves and/or tunnelling photons, and with the "localized Superluminal solutions" to the Maxwell equations (e.g., with the so-called X-shaped ones). The present paper is sketchy, but is followed by a large enough bibliography to allow the interested reader deepening the preferred topic.

physics.pop-ph↗
arXiv1998

On the propagation speed of evanescent modes

The group-velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be Superluminal (v_g > c). By contrast, it is known that the precursor speed in vacuum cannot be larger than c. In this paper, by computer simulations based on Maxwell equations only, we show the existence of both phenomena. In other words, we verify the actual possibility of Superluminal group velocities, without violating the so-called (naive) Einstein causality. (Subject classes: General physics, Classical physics, Optics, Special Relativity; PACS nos.: 73.40Gk, 03.80+z, 03.65Bz; Keywords: evanescent waves; tunnelling photons; Hartman effect; group velocity; Superluminal waves; precursors; transient waves; front velocity; Maxwell equations; electromagnetic waves; computer simulations; Special Relativity; Extended Relativity).

physics.gen-ph↗