6,102 research outputs found
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
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