7,221 research outputs found
Mixed phase and bound states in the phase diagram of the extended Hubbard model
The paper examines part of the ground state diagram of the extended Hubbard
model, with the on-site attraction U0 in the
presence of charge density waves, superconducting and -superconducting
order parameters. We show the possibility of the stabilization of the mixed
state, with all three nonzero order parameters, in the model with nearest
neighbor interactions. The other result of the paper is application of the
exact solution of the Schrodinger equation for the two electron bound state, as
an additional bound for the phase diagram of the model, resulting in the
partial suppression of the superconducting state of the s-wave symmetry, in
favor of the normal state phase.Comment: submitted to Acta Physica Polonica
A Monte Carlo Renormalization Group Approach to the Bak-Sneppen model
A recent renormalization group approach to a modified Bak-Sneppen model is
discussed. We propose a self-consistency condition for the blocking scheme to
be essential for a successful RG-method applied to self-organized criticality.
A new method realizing the RG-approach to the Bak-Sneppen model is presented.
It is based on the Monte-Carlo importance sampling idea. The new technique
performs much faster than the original proposal. Using this technique we
cross-check and improve previous results.Comment: 11 pages, REVTex, 2 Postscript figures include
Price Variations in a Stock Market With Many Agents
Large variations in stock prices happen with sufficient frequency to raise
doubts about existing models, which all fail to account for non-Gaussian
statistics. We construct simple models of a stock market, and argue that the
large variations may be due to a crowd effect, where agents imitate each
other's behavior. The variations over different time scales can be related to
each other in a systematic way, similar to the Levy stable distribution
proposed by Mandelbrot to describe real market indices. In the simplest, least
realistic case, exact results for the statistics of the variations are derived
by mapping onto a model of diffusing and annihilating particles, which has been
solved by quantum field theory methods. When the agents imitate each other and
respond to recent market volatility, different scaling behavior is obtained. In
this case the statistics of price variations is consistent with empirical
observations. The interplay between ``rational'' traders whose behavior is
derived from fundamental analysis of the stock, including dividends, and
``noise traders'', whose behavior is governed solely by studying the market
dynamics, is investigated. When the relative number of rational traders is
small, ``bubbles'' often occur, where the market price moves outside the range
justified by fundamental market analysis. When the number of rational traders
is larger, the market price is generally locked within the price range they
define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted
to J. Math. Eco
Different hierarchy of avalanches observed in the Bak-Sneppen evolution model
We introduce a new quantity, average fitness, into the Bak-Sneppen evolution
model. Through the new quantity, a different hierarchy of avalanches is
observed. The gap equation, in terms of the average fitness, is presented to
describe the self-organization of the model. It is found that the critical
value of the average fitness can be exactly obtained. Based on the simulations,
two critical exponents, avalanche distribution and avalanche dimension, of the
new avalanches are given.Comment: 5 pages, 3 figure
Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model
Infinite hierarchy of exact equations are derived for the newly-observed
f-avalanche in the Bak-Sneppen evolution model. By solving the first order
exact equation, we found that the critical exponent which governs the
divergence of the average avalanche size, is exactly 1 (for all dimensions),
confirmed by the simulations. Solution of the gap equation yields another
universal exponent, denoting the the relaxation to the attractor, is exactly 1.
We also establish some scaling relations among the critical exponents of the
new avalanche.Comment: 5 pages, 1 figur
Dual of Big-bang and Big-crunch
Starting from the Janus solution and its gauge theory dual, we obtain the
dual gauge theory description of the cosmological solution by procedure of the
double anaytic continuation. The coupling is driven either to zero or to
infinity at the big-bang and big-crunch singularities, which are shown to be
related by the S-duality symmetry. In the dual Yang-Mills theory description,
these are non singular at all as the coupling goes to zero in the N=4 Super
Yang-Mills theory. The cosmological singularities simply signal the failure of
the supergravity description of the full type IIB superstring theory.Comment: 18 pages, 5 figures, references added, minor corrections, further
minor corrections, v4: some clarification and more details adde
Self-organization of structures and networks from merging and small-scale fluctuations
We discuss merging-and-creation as a self-organizing process for scale-free
topologies in networks. Three power-law classes characterized by the power-law
exponents 3/2, 2 and 5/2 are identified and the process is generalized to
networks. In the network context the merging can be viewed as a consequence of
optimization related to more efficient signaling.Comment: Physica A: Statistical Mechanics and its Applications, In Pres
A Heavenly Example of Scale Free Networks and Self-Organized Criticality
The sun provides an explosive, heavenly example of self-organized
criticality. Sudden bursts of intense radiation emanate from rapid
rearrangements of the magnetic field network in the corona. Avalanches are
triggered by loops of flux that reconnect or snap into lower energy
configurations when they are overly stressed. Our recent analysis of
observational data reveals that the loops (links) and footpoints (nodes), where
they attach on the photosphere, embody a scale free network. The statistics of
the avalanches and of the network structure are unified through a simple
dynamical model where the avalanches and network co-generate each other into a
complex, critical state. This particular example points toward a general
dynamical mechanism for self-generation of complex networks.Comment: Submitted to proceedings for the Latin American Workshop on Nonlinear
Phenomena, Salvador, Brazil (2003
Spatial-temporal correlations in the process to self-organized criticality
A new type of spatial-temporal correlation in the process approaching to the
self-organized criticality is investigated for the two simple models for
biological evolution. The change behaviors of the position with minimum barrier
are shown to be quantitatively different in the two models. Different results
of the correlation are given for the two models. We argue that the correlation
can be used, together with the power-law distributions, as criteria for
self-organized criticality.Comment: 3 pages in RevTeX, 3 eps figure
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