63 research outputs found
Deformed oscillator algebras for two dimensional quantum superintegrable systems
Quantum superintegrable systems in two dimensions are obtained from their
classical counterparts, the quantum integrals of motion being obtained from the
corresponding classical integrals by a symmetrization procedure. For each
quantum superintegrable systema deformed oscillator algebra, characterized by a
structure function specific for each system, is constructed, the generators of
the algebra being functions of the quantum integrals of motion. The energy
eigenvalues corresponding to a state with finite dimensional degeneracy can
then be obtained in an economical way from solving a system of two equations
satisfied by the structure function, the results being in agreement to the ones
obtained from the solution of the relevant Schrodinger equation. The method
shows how quantum algebraic techniques can simplify the study of quantum
superintegrable systems, especially in two dimensions.Comment: 22 pages, THES-TP 10/93, hep-the/yymmnn
Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective
A unified vision of the symmetric coupling of angular momenta and of the
quantum mechanical volume operator is illustrated. The focus is on the quantum
mechanical angular momentum theory of Wigner's 6j symbols and on the volume
operator of the symmetric coupling in spin network approaches: here, crucial to
our presentation are an appreciation of the role of the Racah sum rule and the
simplification arising from the use of Regge symmetry. The projective geometry
approach permits the introduction of a symmetric representation of a network of
seven spins or angular momenta. Results of extensive computational
investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International
Conference on Computational Science and Application
Connection Between Type A and E Factorizations and Construction of Satellite Algebras
Recently, we introduced a new class of symmetry algebras, called satellite
algebras, which connect with one another wavefunctions belonging to different
potentials of a given family, and corresponding to different energy
eigenvalues. Here the role of the factorization method in the construction of
such algebras is investigated. A general procedure for determining an so(2,2)
or so(2,1) satellite algebra for all the Hamiltonians that admit a type E
factorization is proposed. Such a procedure is based on the known relationship
between type A and E factorizations, combined with an algebraization similar to
that used in the construction of potential algebras. It is illustrated with the
examples of the generalized Morse potential, the Rosen-Morse potential, the
Kepler problem in a space of constant negative curvature, and, in each case,
the conserved quantity is identified. It should be stressed that the method
proposed is fairly general since the other factorization types may be
considered as limiting cases of type A or E factorizations.Comment: 20 pages, LaTeX, no figure, to be published in J. Phys.
Infinite families of superintegrable systems separable in subgroup coordinates
A method is presented that makes it possible to embed a subgroup separable
superintegrable system into an infinite family of systems that are integrable
and exactly-solvable. It is shown that in two dimensional Euclidean or
pseudo-Euclidean spaces the method also preserves superintegrability. Two
infinite families of classical and quantum superintegrable systems are obtained
in two-dimensional pseudo-Euclidean space whose classical trajectories and
quantum eigenfunctions are investigated. In particular, the wave-functions are
expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure
Casimir Effect as a Test for Thermal Corrections and Hypothetical Long-Range Interactions
We have performed a precise experimental determination of the Casimir
pressure between two gold-coated parallel plates by means of a micromachined
oscillator. In contrast to all previous experiments on the Casimir effect,
where a small relative error (varying from 1% to 15%) was achieved only at the
shortest separation, our smallest experimental error (%) is achieved
over a wide separation range from 170 nm to 300 nm at 95% confidence. We have
formulated a rigorous metrological procedure for the comparison of experiment
and theory without resorting to the previously used root-mean-square deviation,
which has been criticized in the literature. This enables us to discriminate
among different competing theories of the thermal Casimir force, and to resolve
a thermodynamic puzzle arising from the application of Lifshitz theory to real
metals. Our results lead to a more rigorous approach for obtaining constraints
on hypothetical long-range interactions predicted by extra-dimensional physics
and other extensions of the Standard Model. In particular, the constraints on
non-Newtonian gravity are strengthened by up to a factor of 20 in a wide
interaction range at 95% confidence.Comment: 17 pages, 7 figures, Sixth Alexander Friedmann International Seminar
on Gravitation and Cosmolog
Families of superintegrable Hamiltonians constructed from exceptional polynomials
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose
wave functions are given in terms of Laguerre and exceptional Jacobi
polynomials. The Hamiltonians contain purely quantum terms which vanish in the
classical limit leaving only a previously known family of superintegrable
systems. Additional, higher-order integrals of motion are constructed from
ladder operators for the considered orthogonal polynomials proving the quantum
system to be superintegrable
From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation
Within the quantum affine algebra representation theory we construct linear
covariant operators that generate the Askey-Wilson algebra. It has the property
of a coideal subalgebra, which can be interpreted as the boundary symmetry
algebra of a model with quantum affine symmetry in the bulk. The generators of
the Askey-Wilson algebra are implemented to construct an operator valued -
matrix, a solution of a spectral dependent reflection equation. We consider the
open driven diffusive system where the Askey-Wilson algebra arises as a
boundary symmetry and can be used for an exact solution of the model in the
stationary state. We discuss the possibility of a solution beyond the
stationary state on the basis of the proposed relation of the Askey-Wilson
algebra to the reflection equation
Higher Order Quantum Superintegrability: a new "Painlev\'e conjecture"
We review recent results on superintegrable quantum systems in a
two-dimensional Euclidean space with the following properties. They are
integrable because they allow the separation of variables in Cartesian
coordinates and hence allow a specific integral of motion that is a second
order polynomial in the momenta. Moreover, they are superintegrable because
they allow an additional integral of order . Two types of such
superintegrable potentials exist. The first type consists of "standard
potentials" that satisfy linear differential equations. The second type
consists of "exotic potentials" that satisfy nonlinear equations. For , 4
and 5 these equations have the Painlev\'e property. We conjecture that this is
true for all . The two integrals X and Y commute with the Hamiltonian,
but not with each other. Together they generate a polynomial algebra (for any
) of integrals of motion. We show how this algebra can be used to calculate
the energy spectrum and the wave functions.Comment: 23 pages, submitted as a contribution to the monographic volume
"Integrability, Supersymmetry and Coherent States", a volume in honour of
Professor V\'eronique Hussin. arXiv admin note: text overlap with
arXiv:1703.0975
Examination of plasma-arc skull melting
Translated from Russian (Report of the E.O. Paton Electric Welding Inst., National Academy of Science of the Ukraine, Kiev, 1998)Available from British Library Document Supply Centre-DSC:9023.190(VR-Trans--8744)T / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo
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