12,650 research outputs found
Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions
It is shown that the eigenvalue problem for the hermitian Wilson-Dirac
operator of for a uniform magnetic field in two dimensions can be reduced to
one-dimensional problem described by a relativistic analog of the Harper
equation. An explicit formula for the secular equations is given in term of a
set of polynomials. The spectrum exhibits a fractal structure in the infinite
volume limit. An exact result concerning the index theorem for the overlap
Dirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction
Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
In a unified viewpoint in quantum channel estimation, we compare the
Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the
group covariant model. For this purpose, we introduce the local asymptotic
mini-max bound, whose maximum is shown to be equal to the asymptotic limit of
the mini-max bound. It is shown that the local asymptotic mini-max bound is
strictly larger than the Cramer-Rao bound in the phase estimation case while
the both bounds coincide when the minimum mean square error decreases with the
order O(1/n). We also derive a sufficient condition for that the minimum mean
square error decreases with the order O(1/n).Comment: In this revision, some unlcear parts are clarifie
Triton binding energy calculated from the SU_6 quark-model nucleon-nucleon interaction
Properties of the three-nucleon bound state are examined in the Faddeev
formalism, in which the quark-model nucleon-nucleon interaction is explicitly
incorporated to calculate the off-shell T-matrix. The most recent version,
fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy
^3H=-8.514 MeV in the 34 channel calculation, when the np interaction is used
for the nucleon-nucleon interaction. The charge root mean square radii of the
^3H and ^3He are 1.72 fm and 1.90 fm, respectively, including the finite size
correction of the nucleons. These values are the closest to the experiments
among many results obtained by detailed Faddeev calculations employing modern
realistic nucleon-nucleon interaction models.Comment: 10 pages, no figure
Hybridization Mechanism for Cohesion of Cd-based Quasicrystals
Cohesion mechanism of cubic approximant crystals of newly discovered binary
quasicrystals, CdM (M=Yb and Ca), are studied theoretically. It is found
that stabilization due to alloying is obtained if M is an element with
low-lying unoccupied states. This leads to conclusion that the cohesion of
the Cd-based compounds is due to the hybridization of the states of Yb and
Ca with a wide band. %unlike known stable quasicrystals without transition
elements %such as Al-Li-Cu and Zn-Mg-RE (RE:rare earth). Although a diameter of
the Fermi sphere coincides with the strong Bragg peaks for Cd-Yb and Cd-Ca, the
Hume-Rothery mechanism does not play a principal role in the stability because
neither distinct pseudogap nor stabilization due to alloying is obtained for
isostructural Cd-Mg. In addition to the electronic origin, matching of the
atomic size is very crucial for the quasicrystal formation of the Cd-based
compounds. It is suggested that the glue atoms, which do not participate in the
icosahedral cluster, play an important role in stabilization of the compound.Comment: 4 pages, 2 figure
Probing the qudit depolarizing channel
For the quantum depolarizing channel with any finite dimension, we compare
three schemes for channel identification: unentangled probes, probes maximally
entangled with an external ancilla, and maximally entangled probe pairs. This
comparison includes cases where the ancilla is itself depolarizing and where
the probe is circulated back through the channel before measurement. Compared
on the basis of (quantum Fisher) information gained per channel use, we find
broadly that entanglement with an ancilla dominates the other two schemes, but
only if entanglement is cheap relative to the cost per channel use and only if
the external ancilla is well shielded from depolarization. We arrive at these
results by a relatively simple analytical means. A separate, more complicated
analysis for partially entangled probes shows for the qudit depolarizing
channel that any amount of probe entanglement is advantageous and that the
greatest advantage comes with maximal entanglement
Optimal design of injection mold for plastic bonded magnet
The optimal design of an injection mold for producing a stronger multipole magnet is carried out using the finite element method and the direct search method. It is shown that the maximum flux density in the cavity obtained by the optimal design is about 2.6 times higher than that of the initial shape determined empirically. 3-D analysis of the nonlinear magnetic field in the injection mold with complicated structure is also carried out. The calculated flux distribution on the cavity surface is in good agreement with the measured one</p
Charmless Final State Interaction in B-> pi pi decays
We estimate effects of the final state interactions in B -> pi pi decays
coming from rescattering of pi pi via exchange of rho, sigma, f_0 mesons. Then
we include the rho rho rescattering via exchange of pi, omega, a_1 mesons and
finally we consider contributions of the a_1 pi rescattering via exchange of
rho. The absorptive parts of amplitudes for these processes are determined. In
the case of pi^+ pi^- decay mode, due to model uncertainties, the calculated
contribution is |M_A| =< 1.7 x 10^-8 GeV. This produces a small relative strong
phase for the tree and color-suppressed B -> pi pi amplitudes consistent with
the result of a recent phenomenological analysis based on the BaBar and Belle
results for the B -> pi pi branching ratios and CP asymmetries.Comment: 10 pages, 2 figure
A Phase-Space Approach to Collisionless Stellar Systems Using a Particle Method
A particle method for reproducing the phase space of collisionless stellar
systems is described. The key idea originates in Liouville's theorem which
states that the distribution function (DF) at time t can be derived from
tracing necessary orbits back to t=0. To make this procedure feasible, a
self-consistent field (SCF) method for solving Poisson's equation is adopted to
compute the orbits of arbitrary stars. As an example, for the violent
relaxation of a uniform-density sphere, the phase-space evolution which the
current method generates is compared to that obtained with a phase-space method
for integrating the collisionless Boltzmann equation, on the assumption of
spherical symmetry. Then, excellent agreement is found between the two methods
if an optimal basis set for the SCF technique is chosen. Since this
reproduction method requires only the functional form of initial DFs but needs
no assumptions about symmetry of the system, the success in reproducing the
phase-space evolution implies that there would be no need of directly solving
the collisionless Boltzmann equation in order to access phase space even for
systems without any special symmetries. The effects of basis sets used in SCF
simulations on the reproduced phase space are also discussed.Comment: 16 pages w/4 embedded PS figures. Uses aaspp4.sty (AASLaTeX v4.0). To
be published in ApJ, Oct. 1, 1997. This preprint is also available at
http://www.sue.shiga-u.ac.jp/WWW/prof/hozumi/papers.htm
Differential Geometry of Group Lattices
In a series of publications we developed "differential geometry" on discrete
sets based on concepts of noncommutative geometry. In particular, it turned out
that first order differential calculi (over the algebra of functions) on a
discrete set are in bijective correspondence with digraph structures where the
vertices are given by the elements of the set. A particular class of digraphs
are Cayley graphs, also known as group lattices. They are determined by a
discrete group G and a finite subset S. There is a distinguished subclass of
"bicovariant" Cayley graphs with the property that ad(S)S is contained in S.
We explore the properties of differential calculi which arise from Cayley
graphs via the above correspondence. The first order calculi extend to higher
orders and then allow to introduce further differential geometric structures.
Furthermore, we explore the properties of "discrete" vector fields which
describe deterministic flows on group lattices. A Lie derivative with respect
to a discrete vector field and an inner product with forms is defined. The
Lie-Cartan identity then holds on all forms for a certain subclass of discrete
vector fields.
We develop elements of gauge theory and construct an analogue of the lattice
gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear
connections are considered and a simple geometric interpretation of the torsion
is established.
By taking a quotient with respect to some subgroup of the discrete group,
generalized differential calculi associated with so-called Schreier diagrams
are obtained.Comment: 51 pages, 11 figure
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