Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry

We study the inequivalent quantizations of the N = 3 Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts. Our inequivalent quantizations respect the ` mirror-S_3\rq\ invariance (which realizes the symmetry under the cyclic permutations of the particles) and the scale invariance in the limit of vanishing harmonic potential. We find a two-parameter family of novel quantizations in the angular part and classify the eigenstates in terms of the irreducible representations of the S_3 group. The scale invariance restricts the quantization in the radial part uniquely, except for the eigenstates coupled to the lowest two angular levels for which two types of boundary conditions are allowed independently from all upper levels. It is also found that the eigenvalues corresponding to the singlet representations of the S_3 are universal (parameter-independent) in the family, whereas those corresponding to the doublets of the S_3 are dependent on one of the parameters. These properties are shown to be a consequence of the spectral preserving SU(2) (or its subrgoup U(1)) transformations allowed in the family of inequivalent quantizations.Comment: 24 pages, LaTe

A New Estimation of Mass Accumulation Efficiency in Helium Shell Flashes toward Type Ia Supernova Explosions

We have calculated the mass accumulation efficiency during helium shell flashes to examine whether or not a carbon-oxygen white dwarf (C+O WD) grows up to the Chandrasekhar mass limit to ignite a Type Ia supernova explosion. It has been frequently argued that luminous super-soft X-ray sources and symbiotic stars are progenitors of SNe Ia. In such systems, a C+O WD accretes hydrogen-rich matter from a companion and burns hydrogen steadily on its surface. The WD develops a helium layer underneath the hydrogen-rich envelope and undergoes periodic helium shell flashes. Using OPAL opacity, we have reanalyzed a full cycle of helium shell flashes on a 1.3 M_\odot C+O WD and confirmed that the helium envelope of the WD expands to blow a strong wind. A part of the accumulated matter is lost by the wind. The mass accumulation efficiency is estimated as \eta_{He} = -0.175 (\log \dot M + 5.35)^2 + 1.05, for -7.3 < \log \dot M < -5.9, where the mass accretion rate \dot M is in units of M_\odot yr^{-1}. In relatively high mass accretion rates as expected in recent SN Ia progenitor models, the mass accumulation efficiency is large enough for C+O WDs to grow to the Chandrasekhar mass, i.e., \eta_{He} = 0.9 for \log \dot M = -6.3, and \eta_{He}=0.57 for \log \dot M = -7.0. The wind velocity (\sim 1000 km/s) is much faster than the orbital velocity of the binary (< 300 km/s) and therefore, the wind cannot be accelerated further by the companion's motion.Comment: 11 pages including 4 eps-files, accepted for publication in ApJ Letter

A Modeling of the Super-Eddington Luminosity in Nova Outbursts: V1974 Cygni

We have modeled nova light curves exceeding the Eddington luminosity. It has been suggested that a porous structure develops in nova envelopes during the super Eddington phase and the effective opacity is much reduced for such a porous atmosphere. Based on this reduced opacity model, we have calculated envelope structures and light curves of novae. The optically thick wind model is used to simulate nova winds. We find that the photospheric luminosity and the wind mass-loss rate increase inversely proportional to the reducing factor of opacities, but the wind velocity hardly changes. We also reproduce the optical light curve of V1974 Cygni (Nova Cygni 1992) in the super-Eddington phase, which lasts 13 days from the optical peak 1.7 mag above the Eddington luminosity.Comment: 8 pages, 4 figures, to appear in ApJ

Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

A planar calculus for infinite index subfactors

We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.Comment: 56 pages, many figure

Novel Orbital Ordering induced by Anisotropic Stress in a Manganite Thin Film

We performed resonant and nonresonant x-ray diffraction studies of a Nd0.5Sr0.5MnO3 thin film that exhibits a clear first-order transition. Lattice parameters vary drastically at the metal-insulator transition at 170K (=T_MI), and superlattice reflections appear below 140K (=T_CO). The electronic structure between T_MI and T_CO is identified as A-type antiferromagnetic with the d_{x2-y2} ferroorbital ordering. Below T_CO, a new type of antiferroorbital ordering emerges. The accommodation of the large lattice distortion at the first-order phase transition and the appearance of the novel orbital ordering are brought about by the anisotropy in the substrate, a new parameter for the phase control.Comment: 4pages, 4figure

On local boundary CFT and non-local CFT on the boundary

The holographic relation between local boundary conformal quantum field theories (BCFT) and their non-local boundary restrictions is reviewed, and non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067 with R. Long