3,415 research outputs found
Nucleation theory and the phase diagram of the magnetization-reversal transition
The phase diagram of the dynamic magnetization-reversal transition in pure
Ising systems under a pulsed field competing with the existing order can be
explained satisfactorily using the classical nucleation theory. Indications of
single-domain and multi-domain nucleation and of the corresponding changes in
the nucleation rates are clearly observed. The nature of the second time scale
of relaxation, apart from the field driven nucleation time, and the origin of
its unusual large values at the phase boundary are explained from the
disappearing tendency of kinks on the domain wall surfaces after the withdrawal
of the pulse. The possibility of scaling behaviour in the multi-domain regime
is identified and compared with the earlier observations.Comment: 10 pages Latex, 4 Postscript figure
Statistics of the Kolkata Paise Restaurant Problem
We study the dynamics of a few stochastic learning strategies for the
'Kolkata Paise Restaurant' problem, where N agents choose among N equally
priced but differently ranked restaurants every evening such that each agent
tries get to dinner in the best restaurant (each serving only one customer and
the rest arriving there going without dinner that evening). We consider the
learning strategies to be similar for all the agents and assume that each
follow the same probabilistic or stochastic strategy dependent on the
information of the past successes in the game. We show that some 'naive'
strategies lead to much better utilization of the services than some relatively
'smarter' strategies. We also show that the service utilization fraction as
high as 0.80 can result for a stochastic strategy, where each agent sticks to
his past choice (independent of success achieved or not; with probability
decreasing inversely in the past crowd size). The numerical results for
utilization fraction of the services in some limiting cases are analytically
examined.Comment: 10 pages, 3 figs; accepted in New J Phy
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
From Majorana Fermions to Topological Order
We consider a system consisting of a 2D network of links between Majorana
fermions on superconducting islands. We show that the fermionic Hamiltonian
modeling this system is topologically-ordered in a region of parameter space.
In particular we show that Kitaev's toric code emerges in fourth-order
perturbation theory. By using a Jordan-Wigner transformation we can map the
model onto a family of signed 2D Ising models in a transverse field where the
signs (FM or AFM) are determined by additional gauge bits. Our mapping allows
an understanding of the non-perturbative regime and the phase transition to a
non-topological phase. We discuss the physics behind a possible implementation
of this model and argue how it can be used for topological quantum computation
by adiabatic changes in the Hamiltonian.Comment: 4+4 pages, 5 figures. v2 has a new reference and a few new comments.
In v3: yet another new reference and Supplementary Material is renamed
Appendix. In v4: several typos are corrected, to appear in Phys. Rev. Let
Duality for Exotic Bialgebras
In the classification of Hietarinta, three triangular
-matrices lead, via the FRT formalism, to matrix bialgebras which are not
deformations of the trivial one. In this paper, we find the bialgebras which
are in duality with these three exotic matrix bialgebras. We note that the
duality of FRT is not sufficient for the construction of the bialgebras
in duality. We find also the quantum planes corresponding to these bialgebras
both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq
Particle Acceleration and the Production of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks
Relativistic outflows (jets) of matter are commonly observed from systems
containing black holes. The strongest outflows occur in the radio-loud systems,
in which the accretion disk is likely to have an advection-dominated structure.
In these systems, it is clear that the binding energy of the accreting gas is
emitted primarily in the form of particles rather than radiation. However, no
comprehensive model for the disk structure and the associated outflows has yet
been produced. In particular, none of the existing models establishes a direct
physical connection between the presence of the outflows and the action of a
microphysical acceleration mechanism operating in the disk. In this paper we
explore the possibility that the relativistic protons powering the jet are
accelerated at a standing, centrifugally-supported shock in the underlying
accretion disk via the first-order Fermi mechanism. The theoretical analysis
employed here parallels the early studies of cosmic-ray acceleration in
supernova shock waves, and the particle acceleration and disk structure are
treated in a coupled, self-consistent manner based on a rigorous mathematical
approach. We find that first-order Fermi acceleration at standing shocks in
advection-dominated disks proves to be a very efficient means for accelerating
the jet particles. Using physical parameters appropriate for M87 and SgrA*, we
verify that the jet kinetic luminosities computed using our model agree with
estimates based on observations of the sources.Comment: accepted for publication in the Astrophysical Journa
Floating Phase in 2D ANNNI Model
We investigate whether the floating phase (where the correlation length is
infinite and the spin-spin correlation decays algebraically with distance)
exists in the temperature() - frustration parameter () phase diagram
of 2D ANNNI model. To identify this phase, we look for the region where (i)
finite size effect is prominent and (ii) some relevant physical quantity
changes somewhat sharply and this change becomes sharper as the system size
increases. For , the low temperature phase is ferromagnetic and
we study energy and magnetization. For , the low temperature
phase is antiphase and we study energy, layer magnetization, length of domain
walls running along the direction of frustration, number of domain-intercepts
that are of length 2 along the direction of frustration, and the number of
domain walls that do not touch the upper and/or lower boundary. In agreement
with some previous studies, our final conclusion is that, the floating phase
exists, if at all, only along a line.Comment: 9 pages, 17 figure
Static displacements and chemical correlations in alloys
Recent experiments in metallic solid solutions have revealed interesting
correlations between static pair-displacements and the ordering behavior of
these alloys. This paper discusses a simple theoretical model which
successfully explains these observations and which provides a natural framework
for analyzing experimental measurements of pair-displacements and chemical
correlations in solid solutions. The utility and scope of this model is
demonstrated by analyzing results of experiments on and alloys
and results of simulations of and alloys.Comment: 12 page
Duality and Representations for New Exotic Bialgebras
We find the exotic matrix bialgebras which correspond to the two
non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta,
namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14
which are not deformations of the of the classical algebras of functions on
GL(2) or GL(1|1). With this we finalize the classification of the matrix
bialgebras which unital associative algebras generated by four elements. We
also find the corresponding dual bialgebras of these new exotic bialgebras and
study their representation theory in detail. We also discuss in detail a
special case of R_{S1,4} in which the corresponding algebra turns out to be a
special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn;
reference updated; v3: corrections in subsection 3.
- …