arXiv subjects
Publications and source records attributed to Erasmo Recami.
In this paper, we shall provide an analytical solution describing a Frozen Wave beam after passing through a pair of convex lenses with different focal distances.
At the kind request of the Editor of Hadronic Journal, and of TEC/TNRG (Usa), we recall in this article some elementary historical information about the role played by Ettore Majorana[1-17] with regard to the Neutron, and to the Neutrino. Often we do explicitly insert direct quotations from the original written statements --in particular by Edoardo Amaldi[22-24]--, which in some cases, and for some topics, constitute the main available evidence. We also discuss some recent, unjustified rumors about Ettore Majorana and Enrico Fermi. [Keywords: Ettore Majorana; Neutron; Neutrinos; Enrico Fermi; Edoardo Amaldi; Majorana spinors; Majorana algebras; Majorana fermions; Fred Wilczek; History of XX century physics; Reply to unjustified rumors]
In this paper we present a theoretical method, together with its experimental confirmation, to obtain structures of light by connecting diffraction-resistant cylindrical beams of finite lengths and different radii. The resulting "Lego-beams" can assume, on demand, various unprecedented spatial configurations. We also experimentally generate some of them on using a computational holographic technique and a spatial light modulator. Our new, interesting method of linking together various "pieces of light" can find applications in all fields where structured light beams are needed: in particular, such as optical tweezers, e.g. for biological manipulations, optical guiding of atoms, light orbital angular momentum control, holography, lithography, non-linear-optics, interaction of electromagnetic radiation with Bose-Einstein condensates, and so on, besides the field in general of Localized Waves (non-diffracting beams and pulses).
In recent times, we experimentally realized a quite efficient modeling of the shape of diffraction-resistant optical beams; thus generating for the first time the so-called Frozen Waves (FW), whose longitudinal intensity pattern can be arbitrarily chosen, within a prefixed space interval of the propagation axis. Such waves possess a host of potential applications: in medicine, biomedical optics, optical tweezers, atom guiding, remote sensing, tractor beams, optical communications or metrology, and other topics in photonic areas. In this work, we extend our theory of FWs -- which led to beams endowed with a static envelope -- through a dynamic modeling of the FWs, whose shape is now allowed to evolve in time in a predetermined way. And we experimentally create such dynamic FWs in Optics, via a computational holographic technique and a spatial light modulator. Experimental results are here presented for two cases of dynamic FWs, one of the zeroth and the other of higher order, the last one being the most interesting, consisting in a cylindrical surface of light whose geometry changes in space and time.
In this paper we present a panoramic view of the main scientific articles published by Ettore Majorana, the brightest Italian theoretical physicist of the XX century (actually, Enrico Fermi regarded him as the brighest in the world of his time, and compared him to Galileo and Newton; even if to some people Majorana is often known mainly for his mysterious disappearance in 1938, when he was 31). Extensive information and comments are added with regard to the scientific manuscripts left unpublished by him. We also outline his life, the biographical data being based on letters, documents, testimonies discovered or collected by the author during more than four decades, and contained for instance in Recami's 1987 book quoted in the text. Two pictures complete the paper.
On the basis of suitable theoretical grounds, we study and propose Antennas for the generation, in Acoustics, of Non-Diffracting Beams of ultrasound. We start considering for instance a frequency of about 40 kHz, and foresee fair results even for finite apertures endowed with reasonable diameters (e.g., of 1 m), having in mind various possible applications, including remote sensing. Then, we discuss the production in lossy media of ultrasonic beams resisting both diffraction and attenuation. Everything is afterward investigated for the cases in which high-power acoustic transducers are needed (for instance, for detection at a distance -or even explosion- of buried objects, like mines). Keywords: Acoustic Non-Diffracting Beams; Truncated Beams of Ultrasound; Remote sensing; Diffraction, Attenuation, Annular transducers, Bessel beam superposition, High-power ultrasound emitters, Beams resisting diffraction and attenuation, Acoustic Frozen Waves, Detection of buried objects, Explosion of Mines at a distance
We propose in detail Antennas for generating Non-Diffracting Beams of Microwaves, for instance with frequencies of the order of 10 GHz, obtaining fair results even when having recourse to realistic apertures endowed with reasonable diameters. Our first proposal refers mainly to sets of suitable annular slits, having in mind various possible applications, including remote sensing. Our second proposal --which constitutes one of the main aims of this paper-- refers to the alternative, rather simple, use of a Parabolic Reflector, illuminated by a spherical wave source located on the paraboloid axis but slightly displaced with respect to the Focus of the Paraboloid. Such a parabolic reflector yields "extended focus" (non-diffracting) beams. [OCIS codes: 999.9999; 070.7545; 050.1120; 280.0280; 050.1755; 070.0070; 200.0200. Keywords: Non-Diffracting Waves; Microwaves; Remote sensing; Annular Arrays; Bessel beams; Extended focus; Reflecting paraboloids; Parabolic reflectors; Parabolic antennas].
The so-called Localized Waves (LW), and the "Frozen Waves" (FW), have arisen significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction (self-healing) property, after obstacles with size smaller than the antenna's; while the FWs, a sub-class of theirs, offer the possibility of arbitrarily modeling the field longitudinal intensity pattern inside a prefixed interval, for instance 0 < z < L, of the wave propagation axis. More specifically, the FWs are localized fields "at rest", that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization. In this paper we investigate by simulated experiments, various cases of generation of ultrasonic FW fields, with frequency f_o = 1 MHz in a water-like medium, taking account of the effects of attenuation. We present results of FWs for distances up to L=80 mm, in attenuating media with absorption coefficients alpha in the range 70 < alpha < 170 dB/m. Such simulated FW fields are constructed by using a procedure developed by us, via appropriate finite superpositions of monochromatic ultrasonic Bessel beams. We pay due attention to the selection of the FW parameters, constrained by the tight restrictions imposed by experimental Acoustics, and to some practical implications of the transducer design. The energy localization properties of the Frozen Waves can find application even in many medical apparatus, such as bistouries or acoustic tweezers, and for treatment of diseased tissues (in particular, for the destruction of tumor cells, without affecting the surrounding tissues; besides for a safe kidney stone shuttering, etcetera).
Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More specifically, this work starts dealing with: (i) the hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; with (ii) idem, with the introduction of Time and Space operators; and with (iii) the problem of the four-position and four-momentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physical applications of non-selfadjoint (and even non-hermitian) operators are briefly discussed. We mention how non-hermitian operators can indeed be used in physics [as it was done, elsewhere, for describing Unstable States]; and some considerations are added on the cases of the nuclear optical potential, of quantum dissipation, and in particular of an approach to the measurement problem in QM in terms of a "chronon". [This chapter is largely based on work developed, along the years, in collaboration with V.S.Olkhovsky, and, in smaller parts, with P.Smrz, with R.H.A.Farias, and with S.P.Maydanyuk]. PACS numbers: 03.65.Ta; 03.65.-w; 03.65.Pm; 03.70.+k; 03.65.Xp; 03.65.Yz; 11.10.St; 11.10.-z; 11.90.+t; 02.00.00; 03.00.00; 24.10.Ht; 03.65.Yz; 21.60.-u; 11.10.Ef; 03.65.Fd; 02.40.Dr; 98.80.Jk. Keywords: time operator, space-time operator, non-selfadjoint operators, non-hermitian operators, bilinear operators, time operator for discrete energy spectra, time-energy uncertainty relations, Klein-Gordon equation, chronon, quantum dissipation, decoherence, nuclear optical model, cosmology, projective relativity.
Our aim in this paper is to recall some essential points of "Extended special Relativity", now more correctly called "Non-Restricted special Relativity" theory (NRR), and in particular of the extended Maxwell Equations; as well as to set forth some further comments on the basic differences between Cherenkov Radiation and the so-called X-shaped Waves, met within the more recent realm of the Non-diffracting Waves (also known as Localized Waves). The occasion is furnished by some very recent Seshadri's comments[1] on a previous article of ours, titled "Cherenkov radiation versus X-shaped localized waves" (see[2], and arXiv:0807.4301[physics.optics]), and not less on NRR itself. OCIS codes: 320.5550; 350.7420; 070.7345; 350.5500; 070.0070; 100.7410; 050.050; 000.1600; 000.2690; 000.6800; 250.5530; 260.0260. PACS nos.: 41.60.Bq; 03.50.De; 03.30.+p; 41.20;Jb; 04.30.Db; 42.25.-p; 42.25.Fx; 47.35.Rs. Keywords: Non-diffracing Waves; Localized Waves; Cherenkov radiation; X-shaped waves; Wave equations; Bessel beams; Superluminal pulses; Maxwell equations; Special Relativity; Non-restricted Special Relativity; Extended special Relativity; Lorentz transformations; Superluminal point-charges.
In this paper we show how appropriate superpositions of Bessel beams can be successfully used to obtain arbitrary longitudinal intensity patterns of nondiffracting ultrasonic wavefields with very high transverse localization. More precisely, the method here described allows generating longitudinal acoustic pressure fields, whose longitudinal intensity patterns can assume, in principle, any desired shape within a freely chosen interval 0 < z < L of the propagation axis, and that can be endowed in particular with a s t a t i c envelope (within which only the carrier wave propagates). Indeed, it is here demonstrated by computer evaluations that these very special beams of non-attenuated ultrasonic field can be generated in water-like media by means of annular transducers. Such fields "at rest" have been called by us << Acoustic Frozen Waves >> (FW). The paper presents various cases of FWs in water, and investigates their aperture characteristics, such as minimum required size and ring dimensioning, as well as the influence they have on the proper generation of the desired FW patterns. The FWs are particular Localized Solutions to the wave equation that can be used in many applications, like new kinds of devices, such as, e.g., acoustic tweezers or scalpels, and especially various ultrasound medical apparatus; e.g. for attempting the destruction of tumor cells without affecting the preceding and subsequent (and surrounding) tissues. Keywords: Ultrasound; Frozen Waves; Bessel beam superpositions; Non-diffractive waves; Localized Waves; Annular transducers.
In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane waves, gaussian beams, Bessel-Gauss beams, when truncated by finite apertures. One of the byproducts of our mathematical method is that one can get in few seconds, or minutes, high-precision results which normally require quite long times of numerical simulation. The method works in Electromagnetism (Optics, Microwaves,...), as well as in Acoustics. OCIS codes: (999.9999) Non-diffracting waves; (260.1960) Diffraction theory; (070.7545) Wave propagation; (070.0070) Fourier optics and signal processing; (200.0200) Optics in computing; (050.1120) Apertures; (070.1060) Acousto-optical signal processing; (280.0280) Remote sensing and sensors; (050.1755) Computational electromagnetic methods.
We propose in detail Antennas for generating Nondiffracting Beams of Microwaves, for instance with frequencies of the order of few GHz, obtaining fair results even when having recourse to realistic apertures, with a quite reasonable diameter. The present proposal refers to sets of suitable annular slits. The possible applications are various, including remote sensing. The paper is in Italian. [Si propongono in dettaglio Antenne per la generazione di fasci non-diffrattivi di microonde, per frequenze ad esempio dell'ordine della decina di GHz, ottenendo discreti risultati pur ricorrendo ad antenne realistiche di diametro ridotto. La proposta e' quella di usare un set di opportuni Annular Slits. Le applicazioni possibili sono varie, includendo il remore sensing.]
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G and Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation, within standard Quantum Mechanics; and we obtain both approximate and exact solutions, setting forth particular examples for them. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we also demonstrate, therefore, how to obtain finite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. Some physical comments are added.
This agile small "book" (in Italian) is an introduction to the life and work of Ettore Majorana, the brightest Italian theoretical physicist of the XX century, regarded by Enrico Fermi as the best theoretician of his time in the world. It consists of ten smooth chapters, only few of them being moderately technical, and of three Appendices: (i) about his inaugural lecture on physics at the University of Naples; (ii) about some notes of his, on the role of the statistical laws in physics and in the social sciences; and (iii) with a recapitulatory biographic outline. The present material is mainly taken from our previous book "Il Caso Majorana: Epistolario, Documenti, Testimonianze", first published (1987, 1991) by Mondadori, Milan, and recently (2000, 2002, 2008) published by Di Renzo Editore, Rome. That book presented practically all the serious documents existing on Majorana's life & work [indeed, almost all the biographical documents have been discovered or collected, during a few decades, by the present author, who was the first to publish them]. Actually, we might address to such a book (c/o www.direnzo.it, "Arcobaleno" series) all the readers interested in more and deeper information.
Ettore Majorana, perhaps the greatest Italian theoretical physicist of this century (Enrico Fermi compared him to Galilei and Newton), disappeared misteriously from Naples in 1938, when he was 31. In the first part of this work we outline his scientific personality (on the basis of letters, documents, testimonies collected by us in about twenty years) and the significance of some parts of his publications. In the second part of this paper we set forth some brief information about the unpublished scientific manuscripts left by E.Majorana and known to us till this moment (most of which are deposited at the "Domus Galilaeana" in Pisa, Italy), and present a preliminary Catalogue of them prepared in collaboration with M.Baldo and R.Mignani. [The present material is mainly taken from our book "Il Caso Majorana: Epistolario, Documenti, Testimonianze" (Mondadori, Milan, 1987,1991; Di Renzo, Rome, 2000-2008): We address to such a book (c/o www.direnzo.it, "Arcobaleno" series) all the readers interested in more and deeper information; as well as, for more technical topics, to the subsequent volumes reproducing e.g. part of the scientific manuscripts left unpublished by Ettore Majorana: see, for instance, the e-print arXiv:0709.1183v1[physics.hist-ph].]
Aim of this paper is to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non relativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically, this work starts dealing with: (i) the maximal hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; and with: (ii) the problem of the four-position and four-momentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-selfadjoint (and even non-hermitian) operators are discussed: In particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential. [PACS numbers: 03.65.Ta; 03.65.-w; 03.65.Pm; 03.70.+k; 03.65.Xp; 11.10.St; 11.10.-z; 11.90.+t; 02.00.00; 03.00.00; 24.10.Ht; 03.65.Yz; 21.60.-u; 11.10.Ef; 03.65.Fd. Keywords: time operator in quantum mechanics; space-time operator; time-"Hamiltonian"; non-selfadjoint operators; non-hermitian operators; bilinear operators; time operator for discrete energy spectra; time-energy uncertainty relations; unstable states; quasi-hermitian Hamiltonians; Klein-Gordon equation; quantum dissipation; nuclear optical model].
In the FIRST PART we present simple introductions to gaussian and Bessel waves, and to the Localized Waves (LW), pulses or beams, showing the important properties of the latter, and their applications whenever a role is played by a wave-equation (electromagnetism, optics, acoustics, seismology, geophysics, gravitation, elementary particle physics,...). The First Part ends with a historical APPENDIX, recalling how the geometrical methods of Special Relativity (SR) had predicted the most interesting LWs, i.e., the X-shaped pulses; and presenting a bird's-eye view of the experiments performed with evanescent waves (and/or tunnelling photons), and with the "localized Superluminal solutions". In the SECOND PART, after some more theoretical introduction, we develop a Generalized "Bidirectional Decomposition", and obtain several luminal and Superluminal non-diffracting solutions; we get a space-time focusing of X-Shaped pulses; and deal with chirped optical X-shaped pulses in material media. Finally, in the THIRD PART we investigate also the subluminal LWs, which, among the others, allow to emphasize the role of SR, in its extended, or rather non-restricted, formulation. We study in particular the topic of zero-speed waves, endowed with a static envelope: Namely, we show how localized wavefields can be constructed with high transverse localization, and with a longitudinal intensity pattern that assumes any desired shape within a chosen interval of the propagation axis. Such "Frozen Waves" promise to have even more applications. In between, we do not forget to briefly treat the case of not axially-symmetric solutions, in terms of higher order Bessel beams.