A new description of motion of the Fermionic SO(2N+2) top in the classical limit under the quasi-anticommutation relation approximation

The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidian space (N: number of single-particle states of the fermions). The images of fermion annihilation-creation operators must satisfy the canonical anti-commutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree-Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle-hole plus BCS type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation, due to the unpaired-mode effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi anti-commutation-relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters k and l in the Lagrange multipliers can be determined withuout any inconcistency.Comment: 36 pages, no figures, typos corrected, published versio

Direct observation of the effective bending moduli of a fluid membrane: Free-energy cost due to the reference-plane deformations

Effective bending moduli of a fluid membrane are investigated by means of the transfer-matrix method developed in our preceding paper. This method allows us to survey various statistical measures for the partition sum. The role of the statistical measures is arousing much attention, since Pinnow and Helfrich claimed that under a suitable statistical measure, that is, the local mean curvature, the fluid membranes are stiffened, rather than softened, by thermal undulations. In this paper, we propose an efficient method to observe the effective bending moduli directly: We subjected a fluid membrane to a curved reference plane, and from the free-energy cost due to the reference-plane deformations, we read off the effective bending moduli. Accepting the mean-curvature measure, we found that the effective bending rigidity gains even in the case of very flexible membrane (small bare rigidity); it has been rather controversial that for such non-perturbative regime, the analytical prediction does apply. We also incorporate the Gaussian-curvature modulus, and calculated its effective rigidity. Thereby, we found that the effective Gaussian-curvature modulus stays almost scale-invariant. All these features are contrasted with the results under the normal-displacement measure

A Note on the Eigenvalue Problem in the su(1,1)-Algebra

Normalization constant in the eigenstate appearing in the eigenvalue problem of the su(1,1)-algebra is discussed. This normalization constant is expressed in terms of the Gauss' hypergeometric series which is not absolutely convergent. It is proved that this series is obtained as a certain limit of an absolutely convergent series, which was conjectured in the previous paper.Comment: 9 pages, 2 figure

On the Eigenvalue Problem of the su(1,1)-Algebra and the Coupling Scheme of Two su(1,1)-Spins

After recapitulating the eigenvalue problem of the su(1,1)-algebra in the conventional form, the same problem is treated in an unconventional form, in which the eigenvalue is pure imaginary. Further, the coupling scheme of two su(1,1)-spins is discussed in the framework of two possibilities, in which certain new aspects appear. Finally, the coupling scheme developed in this paper is applied to a concrete example, which will serve boson realization of the so(4)- and the so(3,1)-algebra presented in the next paper.Comment: 19 pages, No figur

Time Dependent Pairing Equations for Seniority One Nuclear Systems

When the time dependent Hartree-Fock-Bogoliubov intrinsic equations of motion are solved in the case of seniority one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility to skip from one orbital to another. This unpleasant feature is by-passed with a new set of pairing time dependent equations that allows the possibility that the unpaired nucleon changes its single-particle level. These equations generalize the time dependent Hartree-Fock-Bogoliubov equations of motion by including the Landau-Zener effect. The derivation of these new equations is presented in details. These equations are applied in the case of a superasymmetric fission process, that is, in order to explain the fine structure the 14C emission from 233Ra. A new version of the Woods-Saxon model extended for two-center potentials is used in this context.Comment: 12 pages, 6 figure

Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media

A remarkable recurrent nova in M 31: The 2010 eruption recovered and evidence of a six-month period

The Andromeda Galaxy recurrent nova M31N 2008-12a has been caught in eruption nine times. Six observed eruptions in the seven years from 2008 to 2014 suggested a duty cycle of ~1 year, which makes this the most rapidly recurring system known and the leading single-degenerate Type Ia Supernova progenitor candidate; but no 2010 eruption has been found so far. Here we present evidence supporting the recovery of the 2010 eruption, based on archival images taken at and around the time. We detect the 2010 eruption in a pair of images at 2010 Nov 20.52 UT, with a magnitude of m_R = 17.84 +/- 0.19. The sequence of seven eruptions shows significant indications of a duty cycle slightly shorter than one year, which makes successive eruptions occur progressively earlier in the year. We compared three archival X-ray detections with the well observed multi-wavelength light curve of the 2014 eruption to accurately constrain the time of their optical peaks. The results imply that M31N 2008-12a might have in fact a recurrence period of ~6 months (175 +/- 11 days), making it even more exceptional. If this is the case, then we predict that soon two eruptions per year will be observable. Furthermore, we predict the next eruption will occur around late Sep 2015. We encourage additional observations.Comment: 4 pages, 3 figures, 2 tables; submitted to A&A Letter

Can the frequency-dependent specific heat be measured by thermal effusion methods?

It has recently been shown that plane-plate heat effusion methods devised for wide-frequency specific-heat spectroscopy do not give the isobaric specific heat, but rather the so-called longitudinal specific heat. Here it is shown that heat effusion in a spherical symmetric geometry also involves the longitudinal specific heat.Comment: Paper presented at the Fifth International Workshop on Complex Systems (Sendai, September, 2007), to appear in AIP Conference Proceeding

Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism

A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N =4,5,...,10, we obtain an estimate for the correlation-length critical exponent nu = 0.81(5)

The extinction law from photometric data: linear regression methods

Context. The properties of dust grains, in particular their size distribution, are expected to differ from the interstellar medium to the high-density regions within molecular clouds. Since the extinction at near-infrared wavelengths is caused by dust, the extinction law in cores should depart from that found in low-density environments if the dust grains have different properties. Aims. We explore methods to measure the near-infrared extinction law produced by dense material in molecular cloud cores from photometric data. Methods. Using controlled sets of synthetic and semi-synthetic data, we test several methods for linear regression applied to the specific problem of deriving the extinction law from photometric data. We cover the parameter space appropriate to this type of observations. Results. We find that many of the common linear-regression methods produce biased results when applied to the extinction law from photometric colors. We propose and validate a new method, LinES, as the most reliable for this effect. We explore the use of this method to detect whether or not the extinction law of a given reddened population has a break at some value of extinction.Comment: 15 pages, 18 figures, accepted to A&A, in pres