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

The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model

The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a relativistic theory our previous findings on nonrelativistic oscillator where they were known under the name of `spin-orbit pendulum'. There are important relativistic effects (lack of periodicity, zitterbewegung, negative energy states). Many of them disappear after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate postscript figure

Travelling to exotic places with cavity QED systems

Recent theoretical schemes for utilizing cavity QED models as quantum simulators are reviewed. By considering a quadrature representation for the fields, it is shown how Jahn-Teller models, effective Abelian or non-Abelian gauge potentials, transverse Hall currents, and relativistic effects naturally arise in these systems. Some of the analytical predictions are verified numerically using realistic experimental parameters taking into account for system losses. Thereby demonstrating their feasibility with current experimental setups.Comment: 5 pages, 3 figure

Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory

We describe a strategy for attacking the canonical nuclear structure problem ---bound-state properties of a system of point nucleons interacting via a two-body potential---which involves an expansion in the number of particles scattering at high momenta, but is otherwise exact. The required self-consistent solutions of the Bloch-Horowitz equation for effective interactions and operators are obtained by an efficient Green's function method based on the Lanczos algorithm. We carry out this program for the simplest nuclei, d and $^3$He, to contrast a rigorous effective theory with the shell model, thereby illustrating several of the uncontrolled approximations in the latter.Comment: Revtex; two columns; four pages; two figures; submitted to Phys. Rev. Let

Alternative Mathematical Technique to Determine LS Spectral Terms

We presented an alternative computational method for determining the permitted LS spectral terms arising from $l^N$ electronic configurations. This method makes the direct calculation of LS terms possible. Using only basic algebra, we derived our theory from LS-coupling scheme and Pauli exclusion principle. As an application, we have performed the most complete set of calculations to date of the spectral terms arising from $l^N$ electronic configurations, and the representative results were shown. As another application on deducing LS-coupling rules, for two equivalent electrons, we deduced the famous Even Rule; for three equivalent electrons, we derived a new simple rule.Comment: Submitted to Phys. Rev.

Linear canonical transformations and quantum phase:a unified canonical and algebraic approach

The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action-angle phase space formalism is established and it is shown that the conceptual foundation of the quantum phase problem lies within the algebraic properties of the quantum canonical transformations in the quantum phase space. The representations of the Wigner function in the generalized action-angle unitary operator pair for certain Hamiltonian systems with the dynamical symmetry are examined. This generalized canonical formalism is applied to the quantum harmonic oscillator to examine the properties of the unitary quantum phase operator as well as the action-angle Wigner function.Comment: 19 pages, no figure

Energy spectrum of the relativistic Dirac-Morse problem

We derive an elegant analytic formula for the energy spectrum of the relativistic Dirac-Morse problem, which has been solved recently. The new formula displays the properties of the spectrum more vividly.Comment: Replaced with a more potrable PDF versio

Matter wave pulses characteristics

We study the properties of quantum single-particle wave pulses created by sharp-edged or apodized shutters with single or periodic openings. In particular, we examine the visibility of diffraction fringes depending on evolution time and temperature; the purity of the state depending on the opening-time window; the accuracy of a simplified description which uses ``source'' boundary conditions instead of solving an initial value problem; and the effects of apodization on the energy width.Comment: 11 pages, 11 figure

Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations

The interest of quadratic algebras for position-dependent mass Schr\"odinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional radial harmonic oscillators with $d \ge 2$ and a specific mass choice depending on some positive parameter $\alpha$. Via some minor changes, the one-dimensional oscillator on the line with the same kind of mass is included in this class. The existence of a single unitary irreducible representation belonging to the positive-discrete series type for $d \ge 2$ and of two of them for d=1 is proved. The transition to the constant-mass limit $\alpha \to 0$ is studied and deformed su(1,1) generators are constructed. These operators are finally used to generate all the bound-state wavefunctions by an algebraic procedure.Comment: 21 pages, no figure, 2 misprints corrected; published versio

Atom laser dynamics in a tight-waveguide

We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. During the time evolution the density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir.Comment: 6 pages, 5 figures, to be published in the Proceedings of the 395th WE-Heraeus Seminar on "Time Dependent Phenomena in Quantum Mechanics ", organized by T. Kramer and M. Kleber (Blaubeuren, Germany, September 2007