Spectral analysis of a massless charged scalar field with spacial cut-off

The quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, the Hamiltonian of the system is realized as a linear operator on a boson Fock space. It is proven that the Hamiltonian strongly commutes with the total charge operator. This fact implies that the state space of the charged scalar field is decomposed into the infinite direct sum of fixed total charge spaces. Moreover, under certain conditions, the Hamiltonian is bounded below, self-adjoint and has a ground ground state for an arbitrarily coupling constant. A relation between the total charge of the ground state and a number operator bound is also revealed

On Weyl modules of cyclotomic qq-Schur algebras

We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule. We also study corresponding symmetric functions. Finally, we give some simple applications to modular representations of cyclotomic $q$-Schur algebras.Comment: 28 page

Radiation-driven Fountain and Origin of Torus around Active Galactic Nuclei

We propose a plausible mechanism to explain the formation of the so-called "obscuring tori" around active galactic nuclei (AGNs) based on three-dimensional hydrodynamic simulations including radiative feedback from the central source. The X-ray heating and radiation pressure on the gas are explicitly calculated using a ray-tracing method. This radiation feedback drives a "fountain", that is, a vertical circulation of gas in the central a few to tens parsecs. Interaction between the non-steady outflows and inflows causes the formation of a geometrically thick torus with internal turbulent motion. As a result, the AGN is obscured for a wide range of solid angles. In a quasi-steady state, the opening angles for the column density toward a black hole < 10^23 cm^-2 are approximately +-30 deg and +-50 deg for AGNs with 10% and 1% Eddington luminosity, respectively. Mass inflows through the torus coexist with the outflow and internal turbulent motion, and the average mass accretion rate to the central parsec region is 2x10^-4 ~ 10^-3, M_sun/yr this is about ten times smaller than accretion rate required to maintain the AGN luminosity. This implies that relatively luminous AGN activity is intrinsically intermittent or that there are other mechanisms, such as stellar energy feedback, that enhance the mass accretion to the center.Comment: 12 pages, 9 figures, accepted publication in Ap