Classes of Bivariate Orthogonal Polynomials

We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-$D$ Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-$D$ Hermite polynomials and a two variable extension of the Zernike or disc polynomials. We also give $q$-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 $q$-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