Gravitational Correction in Neutrino Oscillations

We investigate the quantum mechanical oscillations of neutrinos propagating in weak gravitational field. The correction to the result in the flat space-time is derived.Comment: 5 pages, Latex file without figures , accepted for publication in Modern Physics Letters

Correlations of multiplicities in length spectra for congruence subgroups

Bogomolny-Leyvraz-Schmit (1996) and Peter (2002) proposed an asymptotic formula for the correlation of the multiplicities in length spectrum on the modular surface, and Lukianov (2007) extended its asymptotic formula to the Riemann surfaces derived from the congruence subgroup \Gam_0(n) and the quaternion type co-compact arithmetic groups. The coefficients of the leading terms in these asymptotic formulas are described in terms of Euler products over prime numbers, and they appear in eigenvalue statistic formulas found by Rudnick (2005) and Lukianov (2007) for the Laplace-Beltrami operators on the corresponding Riemann surfaces. In the present paper, we further extend their asymptotic formulas to the higher level correlations of the multiplicities for any congruence subgroup of the modular group.Comment: 17 page

Chiral symmetry restoration in monolayer graphene induced by Kekule distortion

We propose a chiral symmetry restoration mechanism in monolayer graphene, in analogy with the strongly coupled gauge theory. The chiral (sublattice) symmetry of graphene, which is spontaneously broken under the effectively strong Coulomb interaction, is restored by introducing the Kekule-patterned lattice distortion externally. Such a phase transition is investigated analytically by the lattice gauge theory model with the original honeycomb lattice structure. We discuss the relation between the chiral phase transition and the spectral gap amplitude.Comment: 4 pages, 3 figures; published versio

Quasi-toroidal oscillations in rotating relativistic stars

Quasi-toroidal oscillations in slowly rotating stars are examined in the framework of general relativity. The oscillation frequency to first order of the rotation rate is not a single value even for uniform rotation unlike the Newtonian case. All the oscillation frequencies of the r-modes are purely neutral and form a continuous spectrum limited to a certain range. The allowed frequencies are determined by the resonance condition between the perturbation and background mean flow. The resonant frequency varies with the radius according to general relativistic dragging effect.Comment: 4 pages, Latex file without figure, submitted to Mon. Not. R. Astron. So