1,447 research outputs found
Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras
The concept of biperfect (noncocommutative) weak Hopf algebras is introduced
and their properties are discussed. A new type of quasi-bicrossed products are
constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which
are generalizations of the Hopf pairs introduced by Takeuchi. As a special
case, the quantum double of a finite dimensional biperfect (noncocommutative)
weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid
as well as a noncommutative and noncocommutative weak Hopf algebra are given,
generalizing quantum doubles from a group and a noncommutative and
noncocommutative Hopf algebra, respectively. Moreover, some characterisations
of quantum doubles of finite dimensional biperfect weak Hopf algebras are
obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need
pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty
Tunneling splitting of magnetic levels in Fe8 detected by 1H NMR cross relaxation
Measurements of proton NMR and the spin lattice relaxation rate 1/T1 in the
octanuclear iron (III) cluster [Fe8(N3C6H15)6O2(OH)12][Br8 9H2O], in short Fe8,
have been performed at 1.5 K in a powder sample aligned along the main
anisotropy z axis, as a function of a transverse magnetic field (i.e.,
perpendicular to the main easy axis z). A big enhancement of 1/T1 is observed
over a wide range of fields (2.5-5 T), which can be attributed to the tunneling
dynamics; in fact, when the tunneling splitting of the pairwise degenerate
m=+-10 states of the Fe8 molecule becomes equal to the proton Larmor frequency
a very effective spin lattice relaxation channel for the nuclei is opened. The
experimental results are explained satisfactorily by considering the
distribution of tunneling splitting resulting from the distribution of the
angles in the hard xy plane for the aligned powder, and the results of the
direct diagonalization of the model Hamiltonian.Comment: J. Appl. Phys., in pres
Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System
Limit theorems for the time average of some observation functions in an
infinite measure dynamical system are studied. It is known that intermittent
phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky
reaction, are described by infinite measure dynamical systems.We show that the
time average of the observation function which is not the function,
whose average with respect to the invariant measure is finite, converges to
the generalized arcsine distribution. This result leads to the novel view that
the correlation function is intrinsically random and does not decay. Moreover,
it is also numerically shown that the time average of the observation function
converges to the stable distribution when the observation function has the
infinite mean.Comment: 8 pages, 8 figure
Coupled Oscillators with Chemotaxis
A simple coupled oscillator system with chemotaxis is introduced to study
morphogenesis of cellular slime molds. The model successfuly explains the
migration of pseudoplasmodium which has been experimentally predicted to be
lead by cells with higher intrinsic frequencies. Results obtained predict that
its velocity attains its maximum value in the interface region between total
locking and partial locking and also suggest possible roles played by partial
synchrony during multicellular development.Comment: 4 pages, 5 figures, latex using jpsj.sty and epsf.sty, to appear in
J. Phys. Soc. Jpn. 67 (1998
New aspects of the Z Z-graded 1D superspace: induced strings and 2D relativistic models
A novel feature of the -graded
supersymmetry which finds no counterpart in ordinary supersymmetry is the
presence of -graded exotic bosons (implied by the existence of two classes
of parafermions). Their interpretation, both physical and mathematical,
presents a challenge. The role of the "exotic bosonic coordinate" was not
considered by previous works on the one-dimensional -graded superspace (which was restricted to produce
point-particle models). By treating this coordinate at par with the other
graded superspace coordinates new consequences are obtained. The graded
superspace calculus of the -graded worldline
super-Poincar\'e algebra induces two-dimensional -graded relativistic models; they are invariant under a new -graded super-Poincar\'e algebra which differs
from the previous two -graded versions
of super-Poincar\'e introduced in the literature. In this new superalgebra the
second translation generator and the Lorentz boost are -graded.
Furthermore, if the exotic coordinate is compactified on a circle ,
a -graded closed string with periodic
boundary conditions is derived. The analysis of the irreducibility conditions
of the supermultiplet implies that a larger -deformed, where
is a real parameter) class of point-particle models than the ones
discussed so far in the literature (recovered at ) is obtained. While
the spectrum of the point-particle models is degenerate (due to its
relation with an supersymmetry), this is no longer the case for
the models.Comment: 28 page
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