231,141 research outputs found
Classes of Bivariate Orthogonal Polynomials
We introduce a class of orthogonal polynomials in two variables which
generalizes the disc polynomials and the 2- Hermite polynomials. We identify
certain interesting members of this class including a one variable
generalization of the 2- Hermite polynomials and a two variable extension of
the Zernike or disc polynomials. We also give -analogues of all these
extensions. In each case in addition to generating functions and three term
recursions we provide raising and lowering operators and show that the
polynomials are eigenfunctions of second-order partial differential or
-difference operators
Massive uncharged and charged particles' tunneling from the Horowitz-Strominger Dilaton black hole
Originally, Parikh and Wilczek's work is only suitable for the massless
particles' tunneling. But their work has been further extended to the cases of
massive uncharged and charged particles' tunneling recently. In this paper, as
a particular black hole solution, we apply this extended method to reconsider
the tunneling effect of the H.S Dilaton black hole. We investigate the behavior
of both massive uncharged and charged particles, and respectively calculate the
emission rate at the event horizon. Our result shows that their emission rates
are also consistent with the unitary theory. Moreover, comparing with the case
of massless particles' tunneling, we find that this conclusion is independent
of the kind of particles. And it is probably caused by the underlying
relationship between this method and the laws of black hole thermodynamics.Comment: 6 pages, no figure, revtex 4, accepted by Int. J. Mod. Phys
Dynamical chiral symmetry breaking in sliding nanotubes
We discovered in simulations of sliding coaxial nanotubes an unanticipated
example of dynamical symmetry breaking taking place at the nanoscale. While
both nanotubes are perfectly left-right symmetric and nonchiral, a nonzero
angular momentum of phonon origin appears spontaneously at a series of critical
sliding velocities, in correspondence with large peaks of the sliding friction.
The non-linear equations governing this phenomenon resemble the rotational
instability of a forced string. However, several new elements, exquisitely
"nano" appear here, with the crucial involvement of Umklapp and of sliding
nanofriction.Comment: To appear in PR
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