Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction

Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac oscillator in its one- and many-body versions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-particle system with a new type of Dirac oscillator interaction of frequency~$\omega$. By considering the latter together with its partner corresponding to the replacement of~$\omega$ by~$-\omega$, we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.Comment: 21 pages, LaTeX, 1 figure (can be obtained from the authors), to appear in J. Phys.

Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics

For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Mass spectra of the particle-antiparticle system with a Dirac oscillator interaction

The present view about the structure of mesons is that they are a quark-antiquark system. The mass spectrum corresponding to this system should, in principle, be given by chromodynamics, but this turns out to be a complex affair. Thus it is of some interest to consider relativistic systems of particle-antiparticle, with a simple type of interaction, which could give some insight on the spectra we can expect for mesons. This analysis is carried out when the interaction is of the Dirac oscillator type. It is shown that the Dirac equation of the antiparticle can be obtained from that of the particle by just changing the frequency omega into -omega. Following a procedure suggested by Barut, the equation for the particle-antiparticle system is derived and it is solved by a perturbation procedure. Thus, explicit expressions for the square of the mass spectra are obtained and its implications in the meson case is discussed

Playing relativistic billiards beyond graphene

The possibility of using hexagonal structures in general and graphene in particular to emulate the Dirac equation is the basis of our considerations. We show that Dirac oscillators with or without restmass can be emulated by distorting a tight binding model on a hexagonal structure. In a quest to make a toy model for such relativistic equations we first show that a hexagonal lattice of attractive potential wells would be a good candidate. First we consider the corresponding one-dimensional model giving rise to a one-dimensional Dirac oscillator, and then construct explicitly the deformations needed in the two-dimensional case. Finally we discuss, how such a model can be implemented as an electromagnetic billiard using arrays of dielectric resonators between two conducting plates that ensure evanescent modes outside the resonators for transversal electric modes, and describe an appropriate experimental setup.Comment: 23 pages, 8 figures. Submitted to NJ

Survival and Nonescape Probabilities for Resonant and Nonresonant Decay

In this paper we study the time evolution of the decay process for a particle confined initially in a finite region of space, extending our analysis given recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly the time-dependent Schroedinger equation for a finite-range potential. We calculate and compare two quantities: (i) the survival probability S(t), i.e., the probability that the particle is in the initial state after a time t; and (ii) the nonescape probability P(t), i.e., the probability that the particle remains confined inside the potential region after a time t. We analyze in detail the resonant and nonresonant decay. In the former case, after a very short time, S(t) and P(t) decay exponentially, but for very long times they decay as a power law, albeit with different exponents. For the nonresonant case we obtain that both quantities differ initially. However, independently of the resonant and nonresonant character of the initial state we always find a transition to the ground state of the system which indicates a process of ``loss of memory'' in the decay.Comment: 26 pages, RevTex file, figures available upon request from [email protected] (To be published in Annals of Physics

Measuring nominal descriptivity

Using Ultan's theory of descriptivity grading as a starting point, I will attempt to capture this differential utility in terms of [...] criteria of literalness, explicitness and syntactic complexity. I will first briefly present his System and investigate some generalizations which he has proposed on the basis of his study of body part terminologies in numerous languages. I will apply his theory to nouns in this and four other semantic domains, in three North American Indian languages. I will test his generalizations and propose some new ones. I will then present an alternative system of descriptivity grading and compare the results of its application with those of Ultan's system. In the final section I will suggest another methodology for quantification. An appendix at the end of the paper lists all of the descriptive lexical items mentioned, graded according to both systems

The Future of Fossils: The Evolution of Paleontological Research in the Modern Age

Dinosaurs are awesome. They hold a special place in everyone’s childhood, and new discoveries in what they looked like and how they lived and might have behaved are exciting news. It’s more common to come across an article unveiling a new fossil as opposed to novel breakthroughs in understanding the paleobiology of these organisms. Although discoveries in the research field are less widespread than field discoveries and new dig sites, even though the datapool of fossils grows every year, new advances in technology allow for new analytical methods to study these fossils. Researchers are now able to test a wider range of more specific hypotheses. Scientific understanding of dinosaurs and how they lived has not progressed as rapidly as would be expected in the new digital age given the abundance of fossils to study. Paleontology is commonly thought of as digging in the field, piecing bones together in a museum, and analyzing morphological characteristics of bones to describe new species. With the new digital age and the development of many distinctions within helpful fields, such as histology, how people think about paleontology and the ways it’s explored can be expanded from just dig sites to include the laboratory setting where even more discoveries happen. Within the professional world of paleontology, there is a lot of discourse over how the field is changing, integrating new technologies, and adapting to be more efficient to researchers in the future. However, amateurs may not be aware of this discussion. My project is designed to investigate what the modern paleontologist does, articulate obstacles the field currently faces, address the plausible solutions that are being, or can 4 be, integrated into the field, and finally to create an online resource for aspiring paleontologists