7,030 research outputs found
A nested sequence of projectors and corresponding braid matrices : (1) Odd dimensions
A basis of projectors, each an matrix with constant
elements, is implemented to construct a class of braid matrices
, being the spectral parameter. Only odd values of
are considered here. Our ansatz for the projectors appearing
in the spectral decomposition of leads to exponentials
as the coefficient of . The sums and
differences of such exponentials on the diagonal and the antidiagonal
respectively provide the nonzero elements of . One
element at the center is normalized to unity. A class of supplementary
constraints imposed by the braid equation leaves free
parameters . The diagonalizer of is presented for
all . Transfer matrices and operators corresponding
to our are studied. Our diagonalizer signals specific
combinations of the components of the operators that lead to a quadratic
algebra of constant matrices. The -dependence factors
out for such combinations. is developed in a power series in
. The basic difference arising for even dimensions is made explicit.
Some special features of our are discussed in a concluding
section.Comment: latex file, 32 page
Fluctuation Cumulant Behavior for the Field-Pulse Induced Magnetisation-Reversal Transition in Ising Models
The universality class of the dynamic magnetisation-reversal transition,
induced by a competing field pulse, in an Ising model on a square lattice,
below its static ordering temperature, is studied here using Monte Carlo
simulations. Fourth order cumulant of the order parameter distribution is
studied for different system sizes around the phase boundary region. The
crossing point of the cumulant (for different system sizes) gives the
transition point and the value of the cumulant at the transition point
indicates the universality class of the transition. The cumulant value at the
crossing point for low temperature and pulse width range is observed to be
significantly less than that for the static transition in the same
two-dimensional Ising model. The finite size scaling behaviour in this range
also indicates a higher correlation length exponent value. For higher
temperature and pulse width range, the transition seems to fall in a mean-field
like universality class.Comment: 5 pages, 8 eps figures, thoroughly revised manuscript with new
figures, accepted in Phys. Rev. E (2003
The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra
Using a contraction procedure, we construct a twist operator that satisfies a
shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2))
algebra. The corresponding universal matrix obeys a
Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a
class of representations, the dynamical Yang-Baxter equation may be expressed
as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure
Length and time scale divergences at the magnetization-reversal transition in the Ising model
The divergences of both the length and time scales, at the magnetization-
reversal transition in Ising model under a pulsed field, have been studied in
the linearized limit of the mean field theory. Both length and time scales are
shown to diverge at the transition point and it has been checked that the
nature of the time scale divergence agrees well with the result obtained from
the numerical solution of the mean field equation of motion. Similar growths in
length and time scales are also observed, as one approaches the transition
point, using Monte Carlo simulations. However, these are not of the same nature
as the mean field case. Nucleation theory provides a qualitative argument which
explains the nature of the time scale growth. To study the nature of growth of
the characteristic length scale, we have looked at the cluster size
distribution of the reversed spin domains and defined a pseudo-correlation
length which has been observed to grow at the phase boundary of the transition.Comment: 9 pages Latex, 3 postscript figure
Particle Acceleration in Advection-Dominated Accretion Disks with Shocks: Green's Function Energy Distribution
The distribution function describing the acceleration of relativistic
particles in an advection-dominated accretion disk is analyzed using a
transport formalism that includes first-order Fermi acceleration, advection,
spatial diffusion, and the escape of particles through the upper and lower
surfaces of the disk. When a centrifugally-supported shock is present in the
disk, the concentrated particle acceleration occurring in the vicinity of the
shock channels a significant fraction of the binding energy of the accreting
gas into a population of relativistic particles. These high-energy particles
diffuse vertically through the disk and escape, carrying away both energy and
entropy and allowing the remaining gas to accrete. The dynamical structure of
the disk/shock system is computed self-consistently using a model previously
developed by the authors that successfully accounts for the production of the
observed relativistic outflows (jets) in M87 and \SgrA. This ensures that the
rate at which energy is carried away from the disk by the escaping relativistic
particles is equal to the drop in the radial energy flux at the shock location,
as required for energy conservation. We investigate the influence of advection,
diffusion, and acceleration on the particle distribution by computing the
nonthermal Green's function, which displays a relatively flat power-law tail at
high energies. We also obtain the energy distribution for the particles
escaping from the disk, and we conclude by discussing the spectrum of the
observable secondary radiation produced by the escaping particles.Comment: Published in Ap
Satellite observations of thought experiments close to a black hole
Since black holes are `black', methods of their identification must
necessarily be indirect. Due to very special boundary condition on the horizon,
the advective flow behaves in a particular way, which includes formation of
centrifugal pressure dominated boundary layer or CENBOL where much of the
infall energy is released and outflows are generated. The observational aspects
of black holes must depend on the steady and time-dependent properties of this
boundary layer. Several observational results are written down in this review
which seem to support the predictions of thought experiments based on this
advective accretion/outflow model. In future, when gravitational waves are
detected, some other predictions of this model could be tested as well.Comment: Published in Classical and Quantum Gravity, v. 17, No. 12, p. 2427,
200
Generalized boson algebra and its entangled bipartite coherent states
Starting with a given generalized boson algebra U_(h(1)) known as the
bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ
the Hopf duality arguments to provide the dually conjugate function algebra
Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a
closed form expression of the universal T matrix that caps the duality and
generalizes the familiar exponential map relating a Lie algebra with its
corresponding group. Subsequently, using an inverse Mellin transform approach,
the coherent states of single-node systems subject to the U_(h(1)) symmetry
are found to be complete with a positive-definite integration measure.
Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to
generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur
Properties of non-BPS SU(3) monopoles
This paper is concerned with magnetic monopole solutions of SU(3)
Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The
different SU(2) embeddings, which correspond to the fundamental monopoles, as
well the embedding along composite root are studied. The interaction of two
different fundamental monopoles is considered. Dissolution of a single
fundamental non-BPS SU(3) monopole in the limit of the minimal symmetry
breaking is analysed.Comment: 19 pages, 7 figures. Typos corrected, reference added. Final version
published in Physica Script
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