323 research outputs found
Long-Time Fluctuations in a Dynamical Model of Stock Market Indices
Financial time series typically exhibit strong fluctuations that cannot be
described by a Gaussian distribution. In recent empirical studies of stock
market indices it was examined whether the distribution P(r) of returns r(tau)
after some time tau can be described by a (truncated) Levy-stable distribution
L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot
be expressed in a closed form, one can identify its parameters by testing the
dependence of the central peak height on tau as well as the power-law decay of
the tails. In an earlier study [Mantegna and Stanley, Nature 376, 46 (1995)] it
was found that the behavior of the central peak of P(r) for the Standard & Poor
500 index is consistent with the Levy distribution with alpha=1.4. In a more
recent study [Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found
that the tails of P(r) exhibit a power-law decay with an exponent alpha ~= 3,
thus deviating from the Levy distribution. In this paper we study the
distribution of returns in a generic model that describes the dynamics of stock
market indices. For the distributions P(r) generated by this model, we observe
that the scaling of the central peak is consistent with a Levy distribution
while the tails exhibit a power-law distribution with an exponent alpha > 2,
namely beyond the range of Levy-stable distributions. Our results are in
agreement with both empirical studies and reconcile the apparent disagreement
between their results
Mesoscopic modelling of financial markets
We derive a mesoscopic description of the behavior of a simple financial
market where the agents can create their own portfolio between two investment
alternatives: a stock and a bond. The model is derived starting from the
Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using
the methods of kinetic theory and consists of a linear Boltzmann equation for
the wealth distribution of the agents coupled with an equation for the price of
the stock. From this model, under a suitable scaling, we derive a Fokker-Planck
equation and show that the equation admits a self-similar lognormal behavior.
Several numerical examples are also reported to validate our analysis
Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements
A generic model of stochastic autocatalytic dynamics with many degrees of
freedom is studied using computer simulations. The time
evolution of the 's combines a random multiplicative dynamics at the individual level with a global coupling through a
constraint which does not allow the 's to fall below a lower cutoff given
by , where is their momentary average and is a
constant. The dynamic variables are found to exhibit a power-law
distribution of the form . The exponent
is quite insensitive to the distribution of the random factor
, but it is non-universal, and increases monotonically as a function
of . The "thermodynamic" limit, N goes to infty and the limit of decoupled
free multiplicative random walks c goes to 0, do not commute:
for any finite while (which is the common range
in empirical systems) for any positive . The time evolution of exhibits intermittent fluctuations parametrized by a (truncated)
L\'evy-stable distribution with the same index . This
non-trivial relation between the distribution of the 's at a given time
and the temporal fluctuations of their average is examined and its relevance to
empirical systems is discussed.Comment: 7 pages, 4 figure
Cutting the same fraction of several measures
We study some measure partition problems: Cut the same positive fraction of
measures in with a hyperplane or find a convex subset of
on which given measures have the same prescribed value. For
both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure
The Magnetic Field of the Solar Corona from Pulsar Observations
We present a novel experiment with the capacity to independently measure both
the electron density and the magnetic field of the solar corona. We achieve
this through measurement of the excess Faraday rotation due to propagation of
the polarised emission from a number of pulsars through the magnetic field of
the solar corona. This method yields independent measures of the integrated
electron density, via dispersion of the pulsed signal and the magnetic field,
via the amount of Faraday rotation. In principle this allows the determination
of the integrated magnetic field through the solar corona along many lines of
sight without any assumptions regarding the electron density distribution. We
present a detection of an increase in the rotation measure of the pulsar
J18012304 of approximately 160 \rad at an elongation of 0.95 from
the centre of the solar disk. This corresponds to a lower limit of the magnetic
field strength along this line of sight of . The lack of
precision in the integrated electron density measurement restricts this result
to a limit, but application of coronal plasma models can further constrain this
to approximately 20mG, along a path passing 2.5 solar radii from the solar
limb. Which is consistent with predictions obtained using extensions to the
Source Surface models published by Wilcox Solar ObservatoryComment: 16 pages, 4 figures (1 colour): Submitted to Solar Physic
One- and many-body effects on mirages in quantum corrals
Recent interesting experiments used scanning tunneling microscopy to study
systems involving Kondo impurities in quantum corrals assembled on Cu or noble
metal surfaces. The solution of the two-dimensional one-particle Schrodinger
equation in a hard wall corral without impurity is useful to predict the
conditions under which the Kondo effect can be projected to a remote location
(the quantum mirage). To model a soft circular corral, we solve this equation
under the potential W*delta(r-r0), where r is the distance to the center of the
corral and r0 its radius. We expand the Green's function of electron surface
states Gs0 for r<r0 as a discrete sum of contributions from single poles at
energies epsilon_i-I*delta_i. The imaginary part delta_i is the half-width of
the resonance produced by the soft confining potential, and turns out to be a
simple increasing function of epsilon_i. In presence of an impurity, we solve
the Anderson model at arbitrary temperatures using the resulting expression for
Gs0 and perturbation theory up to second order in the Coulomb repulsion U. We
calculate the resulting change in the differential conductance Delta dI/dV as a
function of voltage and space, in circular and elliptical corrals, for
different conditions, including those corresponding to recent experiments. The
main features are reproduced. The role of the direct hybridization between
impurity and bulk, the confinement potential, the size of the corral and
temperature on the intensity of the mirage are analyzed. We also calculate
spin-spin correlation functions.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev. B.
Calculations of spin correlations within an additional approximation adde
Structural Probe of a Glass Forming Liquid: Generalized Compressibility
We introduce a new quantity to probe the glass transition. This quantity is a
linear generalized compressibility which depends solely on the positions of the
particles. We have performed a molecular dynamics simulation on a glass forming
liquid consisting of a two component mixture of soft spheres in three
dimensions. As the temperature is lowered (or as the density is increased), the
generalized compressibility drops sharply at the glass transition, with the
drop becoming more and more abrupt as the measurement time increases. At our
longest measurement times, the drop occurs approximately at the mode coupling
temperature . The drop in the linear generalized compressibility occurs at
the same temperature as the peak in the specific heat. By examining the
inherent structure energy as a function of temperature, we find that our
results are consistent with the kinetic view of the glass transition in which
the system falls out of equilibrium. We find no size dependence and no evidence
for a second order phase transition though this does not exclude the
possibility of a phase transition below the observed glass transition
temperature. We discuss the relation between the linear generalized
compressibility and the ordinary isothermal compressibility as well as the
static structure factor.Comment: 18 pages, Latex, 26 encapsulated postscript figures, revised paper is
shorter, to appear in Phys. Rev.
Basic kinetic wealth-exchange models: common features and open problems
We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social
Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati,
Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735],
Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B
17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M.
Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the
equilibrium wealth distributions are proposed. The influence of heterogeneity
is investigated, the appearance of the fat tail in the wealth distribution and
the relaxation to equilibrium are discussed. A unified reformulation of the
models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table
Weakly-Bound Three-Body Systems with No Bound Subsystems
We investigate the domain of coupling constants which achieve binding for a
3-body system, while none of the 2-body subsystems is bound. We derive some
general properties of the shape of the domain, and rigorous upper bounds on its
size, using a Hall--Post decomposition of the Hamiltonian. Numerical
illustrations are provided in the case of a Yukawa potential, using a simple
variational method.Comment: gzipped ps with 11 figures included. To appear in Phys. Rev.
PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation
PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and
generalized harmonic oscillator potentials with the position-dependent mass. A
general point canonical transformation is applied by using a free parameter.
Three different forms of mass distributions are used. A set of the energy
eigenvalues of the bound states and corresponding wave functions for target
potentials are obtained as a function of the free parameter.Comment: 13 page
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