355 research outputs found
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~. By considering the latter together with its
partner corresponding to the replacement of~ by~, 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.
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
Relativistic echo dynamics and the stability of a beam of Landau electrons
We extend the concepts of echo dynamics and fidelity decay to relativistic
quantum mechanics, specifically in the context of Klein-Gordon and Dirac
equations under external electromagnetic fields. In both cases we define
similar expressions for the fidelity amplitude under perturbations of these
fields, and a covariant version of the echo operator. Transformation properties
under the Lorentz group are established. An alternate expression for fidelity
is given in the Dirac case in terms of a 4-current. As an application we study
a beam of Landau electrons perturbed by field inhomogeneities.Comment: 8 pages, no figure
Non-Linear Canonical Transformations in Classical and Quantum Mechanics
-Mechanics is a consistent physical theory which describes both classical
and quantum mechanics simultaneously through the representation theory of the
Heisenberg group. In this paper we describe how non-linear canonical
transformations affect -mechanical observables and states. Using this we
show how canonical transformations change a quantum mechanical system. We seek
an operator on the set of -mechanical observables which corresponds to the
classical canonical transformation. In order to do this we derive a set of
integral equations which when solved will give us the coherent state expansion
of this operator. The motivation for these integral equations comes from the
work of Moshinsky and a variety of collaborators. We consider a number of
examples and discuss the use of these equations for non-bijective
transformations.Comment: The paper has been improved in light of a referee's report. The paper
will appear in the Journal of Mathematical Physics. 24 pages, no figure
The no-core shell model with general radial bases
Calculations in the ab initio no-core shell model (NCSM) have conventionally
been carried out using the harmonic-oscillator many-body basis. However, the
rapid falloff (Gaussian asymptotics) of the oscillator functions at large
radius makes them poorly suited for the description of the asymptotic
properties of the nuclear wavefunction. We establish the foundations for
carrying out no-core configuration interaction (NCCI) calculations using a
basis built from general radial functions and discuss some of the
considerations which enter into using such a basis. In particular, we consider
the Coulomb-Sturmian basis, which provides a complete set of functions with a
realistic (exponential) radial falloff.Comment: 7 pages, 3 figures; presented at Horizons on Innovative Theories,
Experiments, and Supercomputing in Nuclear Physics 2012, New Orleans,
Louisiana, June 4-7, 2012; submitted to J. Phys. Conf. Se
Quantum matter wave dynamics with moving mirrors
When a stationary reflecting wall acting as a perfect mirror for an atomic
beam with well defined incident velocity is suddenly removed, the density
profile develops during the time evolution an oscillatory pattern known as
diffraction in time. The interference fringes are suppressed or their
visibility is diminished by several effects such as averaging over a
distribution of incident velocities, apodization of the aperture function,
atom-atom interactions, imperfect reflection or environmental noise. However,
when the mirror moves with finite velocity along the direction of propagation
of the beam, the visibility of the fringes is enhanced. For mirror velocities
below beam velocity, as used for slowing down the beam, the matter wave splits
into three regions separated by space-time points with classical analogues. For
mirror velocities above beam velocity a visibility enhancement occurs without a
classical counterpart. When the velocity of the beam approaches that of the
mirror the density oscillations rise by a factor 1.8 over the stationary value.Comment: 5.2 pages, 6 figure
Energy Spectrum of a 2D Dirac Oscillator in the Presence of the Aharonov-Bohm Effect
We determine the energy spectrum and the corresponding eigenfunctions of a 2D
Dirac oscillator in the presence of Aharonov-Bohm (AB) effect . It is shown
that the energy spectrum depends on the spin of particle and the AB magnetic
flux parameter. Finally, when the irregular solution occurs it is shown that
the energy takes particular values. The nonrelativistic limit is also
considered.Comment: Latex, 12 page
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
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