A Conjecture about Raising Operators for Macdonald Polynomials

A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser's formula for partitions with length three.Comment: 13 page

Stability of the vortex lattice in D-wave superconductors

Use is made of Onsager's hydrodynamic equation to derive the vibration spectrum of the vortex lattice in d-wave superconductor. In particular the rhombic lattice (i.e. the $45^\circ$ tilted square lattice) is found to be stable for $B>H_{cr}(t)$. Here $H_{cr}(t)$ denotes the critical field at which the vortex lattice transition takes place.Comment: 7 pages, Revte

Surface Shubnikov-de Hass oscillations and non-zero Berry phases of the topological hole conduction in Tl1−x_{1-x}Bi1+x_{1+x}Se2_2

We report the observation of two-dimensional Shubnikov-de Hass (SdH) oscillations in the topological insulator Tl$_{1-x}$Bi$_{1+x}$Se$_2$. Hall effect measurements exhibited electron-hole inversion in samples with bulk insulating properties. The SdH oscillations accompanying the hole conduction yielded a large surface carrier density of $n_{\rm{s}}=5.1 \times10^{12}$/cm$^2$, with the Landau-level fan diagram exhibiting the $\pi$ Berry phase. These results showed the electron-hole reversibility around the in-gap Dirac point and the hole conduction on the surface Dirac cone without involving the bulk metallic conduction.Comment: 5 pages, 4 figure

Exact Solutions for Boson-Fermion Stars in (2+1) dimensions

We solve Einstein equations coupled to a complex scalar field with infinitely large self-interaction, degenerate fermions, and a negative cosmological constant in $(2+1)$ dimensions. Exact solutions for static boson-fermion stars are found when circular symmetry is assumed. We find that the minimum binding energy of boson-fermion star takes a negative value if the value of the cosmological constant is sufficiently small.Comment: 19 pages, 5 figures, RevTeX 3.0, second revised versio