68 research outputs found
Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?
Long memory and volatility clustering are two stylized facts frequently
related to financial markets. Traditionally, these phenomena have been studied
based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and
FIGARCH, inter alia. One advantage of these models is their ability to capture
nonlinear dynamics. Another interesting manner to study the volatility
phenomena is by using measures based on the concept of entropy. In this paper
we investigate the long memory and volatility clustering for the SP 500, NASDAQ
100 and Stoxx 50 indexes in order to compare the US and European Markets.
Additionally, we compare the results from conditionally heteroscedastic models
with those from the entropy measures. In the latter, we examine Shannon
entropy, Renyi entropy and Tsallis entropy. The results corroborate the
previous evidence of nonlinear dynamics in the time series considered.Comment: 8 pages; 2 figures; paper presented in APFA 6 conferenc
Heat Bath Particle Number Spectrum
We calculate the number spectrum of particles radiated during a scattering
into a heat bath using the thermal largest-time equation and the
Dyson-Schwinger equation. We show how one can systematically calculate
{d}/{d\omega} to any order using modified real time
finite-temperature diagrams. Our approach is demonstrated on a simple model
where two scalar particles scatter, within a photon-electron heat bath, into a
pair of charged particles and it is shown how to calculate the resulting
changes in the number spectra of the photons and electrons.Comment: 29 pages, LaTeX; 14 figure
The emergence of Special and Doubly Special Relativity
Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this
paper how a Brownian motion on a short scale can originate a relativistic
motion on scales that are larger than particle's Compton wavelength. This can
be described in terms of polycrystalline vacuum. Viewed in this way, special
relativity is not a primitive concept, but rather it statistically emerges when
a coarse graining average over distances of order, or longer than the Compton
wavelength is taken. By analyzing the robustness of such a special relativity
under small variations in the polycrystalline grain-size distribution we
naturally arrive at the notion of doubly-special relativistic dynamics. In this
way, a previously unsuspected, common statistical origin of the two frameworks
is brought to light. Salient issues such as the role of gauge fixing in
emergent relativity, generalized commutation relations, Hausdorff dimensions of
representative path-integral trajectories and a connection with Feynman
chessboard model are also discussed.Comment: 21 pages, 1 figure, RevTeX4, substantially revised version, accepted
in Phys. Rev.
Deformation quantization of linear dissipative systems
A simple pseudo-Hamiltonian formulation is proposed for the linear
inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics,
our approach is based on the use of non-stationary Poisson brackets, i.e.
corresponding Poisson tensor is allowed to explicitly depend on time. Starting
from this pseudo-Hamiltonian formulation we develop a consistent deformation
quantization procedure involving a non-stationary star-product and an
``extended'' operator of time derivative , differentiating
the -product. As in the usual case, the -algebra of physical
observables is shown to admit an essentially unique (time dependent) trace
functional . Using these ingredients we construct a complete and
fully consistent quantum-mechanical description for any linear dynamical system
with or without dissipation. The general quantization method is exemplified by
the models of damped oscillator and radiating point charge.Comment: 14 pages, typos correcte
Path Integral Approach to 't Hooft's Derivation of Quantum from Classical Physics
We present a path-integral formulation of 't Hooft's derivation of quantum
from classical physics. The crucial ingredient of this formulation is Gozzi et
al.'s supersymmetric path integral of classical mechanics. We quantize
explicitly two simple classical systems: the planar mathematical pendulum and
the Roessler dynamical system.Comment: 29 pages, RevTeX, revised version with minor changes, accepted to
Phys. Rev.
Neutrino damping rate at finite temperature and density
A first principle derivation is given of the neutrino damping rate in
real-time thermal field theory. Starting from the discontinuity of the neutrino
self energy at the two loop level, the damping rate can be expressed as
integrals over space phase of amplitudes squared, weighted with statistical
factors that account for the possibility of particle absorption or emission
from the medium. Specific results for a background composed of neutrinos,
leptons, protons and neutrons are given. Additionally, for the real part of the
dispersion relation we discuss the relation between the results obtained from
the thermal field theory, and those obtained by the thermal average of the
forward scattering amplitude.Comment: LaTex Document, 19 pages, 3 figure
Sub-Planckian black holes and the Generalized Uncertainty Principle
The Black Hole Uncertainty Principle correspondence suggests that there could
exist black holes with mass beneath the Planck scale but radius of order the
Compton scale rather than Schwarzschild scale. We present a modified, self-dual
Schwarzschild-like metric that reproduces desirable aspects of a variety of
disparate models in the sub-Planckian limit, while remaining Schwarzschild in
the large mass limit. The self-dual nature of this solution under naturally implies a Generalized Uncertainty Principle
with the linear form . We also
demonstrate a natural dimensional reduction feature, in that the gravitational
radius and thermodynamics of sub-Planckian objects resemble that of -D
gravity. The temperature of sub-Planckian black holes scales as rather than
but the evaporation of those smaller than g is suppressed by
the cosmic background radiation. This suggests that relics of this mass could
provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy
Superpositions of Probability Distributions
Probability distributions which can be obtained from superpositions of
Gaussian distributions of different variances v = \sigma ^2 play a favored role
in quantum theory and financial markets. Such superpositions need not
necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian
processes because they may introduce memory effects. We derive the general form
of the smearing distributions in v which do not destroy the semigroup property.
The smearing technique has two immediate applications. It permits simplifying
the system of Kramers-Moyal equations for smeared and unsmeared conditional
probabilities, and can be conveniently implemented in the path integral
calculus. In many cases, the superposition of path integrals can be evaluated
much easier than the initial path integral. Three simple examples are
presented, and it is shown how the technique is extended to quantum mechanics.Comment: 23 pages, RevTeX, minor changes, accepted to Phys. Rev.
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