9,112 research outputs found
The Global Anomaly Through Level Circling
We discuss a novel manifestation of the global anomaly in an
gauge theory with an odd number of chiral quark doublets and arbitrary Yukawa
couplings. We argue that the massive 4-dim.() Euclidean Dirac operator is
nonhermitean with its spectrum of eigenvalues lying in
pairs in the complex plane. Consequently the existence of an odd number of
normalizable zero modes of the 5-dim.() massive Dirac operator is
equivalent to a fermionic level exchange phenomenon, level ``circling'', under
continuous topologically nontrivial deformations of the external gauge field.
More generally global anomalies are a manifestation of fermionic level
``circling'' in any gauge theory with an odd number of massive
fermions in the spinor representation and arbitrary Yukawa couplings.Comment: 14 pages, NBI-HE-93-5
On sphaleron deformations induced by Yukawa interactions
Due to the presence of the chiral anomaly sphalerons with Chern-Simons number
a half (CS=1/2) are the only static configurations that allow for a fermion
level crossing in the two-dimensional Abelian-Higgs model with massless
fermions, i.e. in the absence of Yukawa interactions. In the presence of
fermion-Higgs interactions we demonstrate the existence of zero energy
solutions to the one-dimensional Dirac equation at deformed sphalerons with
CS Induced level crossing due to Yukawa interactions illustrates a
non-trivial generalization of the Atiyah-Patodi-Singer index theorem and of the
equivalence between parity anomaly in odd and the chiral anomaly in even
dimensions. We discuss a subtle manifestation of this effect in the standard
electroweak theory at finite temperatures.Comment: 14 pages, Latex, NBI-HE-93-7
Inverse Statistics for Stocks and Markets
In recent publications, the authors have considered inverse statistics of the
Dow Jones Industrial Averaged (DJIA) [1-3]. Specifically, we argued that the
natural candidate for such statistics is the investment horizons distribution.
This is the distribution of waiting times needed to achieve a predefined level
of return obtained from detrended historic asset prices. Such a distribution
typically goes through a maximum at a time coined the {\em optimal investment
horizon}, , which defines the most likely waiting time for
obtaining a given return . By considering equal positive and negative
levels of return, we reported in [2,3] on a quantitative gain/loss asymmetry
most pronounced for short horizons. In the present paper, this gain/loss
asymmetry is re-visited for 2/3 of the individual stocks presently in the DJIA.
We show that this gain/loss asymmetry established for the DJIA surprisingly is
{\em not} present in the time series of the individual stocks. The most
reasonable explanation for this fact is that the gain/loss asymmetry observed
in the DJIA as well as in the SP500 and Nasdaq are due to movements in the
market as a whole, {\it i.e.}, cooperative cascade processes (or
``synchronization'') which disappear in the inverse statistics of the
individual stocks.Comment: Revtex 13 pages, including 15 figure
Stochastics theory of log-periodic patterns
We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge
Global magnetohydrodynamical models of turbulence in protoplanetary disks I. A cylindrical potential on a Cartesian grid and transport of solids
We present global 3D MHD simulations of disks of gas and solids, aiming at
developing models that can be used to study various scenarios of planet
formation and planet-disk interaction in turbulent accretion disks. A second
goal is to show that Cartesian codes are comparable to cylindrical and
spherical ones in handling the magnetohydrodynamics of the disk simulations, as
the disk-in-a-box models presented here develop and sustain MHD turbulence. We
investigate the dependence of the magnetorotational instability on disk scale
height, finding evidence that the turbulence generated by the magnetorotational
instability grows with thermal pressure. The turbulent stresses depend on the
thermal pressure obeying a power law of 0.24+/-0.03, compatible with the value
of 0.25 found in shearing box calculations. The ratio of stresses decreased
with increasing temperature. We also study the dynamics of boulders in the
hydromagnetic turbulence. The vertical turbulent diffusion of the embedded
boulders is comparable to the turbulent viscosity of the flow. Significant
overdensities arise in the solid component as boulders concentrate in high
pressure regions.Comment: Changes after peer review proces
Log-periodic route to fractal functions
Log-periodic oscillations have been found to decorate the usual power law
behavior found to describe the approach to a critical point, when the
continuous scale-invariance symmetry is partially broken into a discrete-scale
invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the
renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes
characterized by the amplitudes A(n) of the power law series expansion. These
two classes are separated by a novel ``critical'' point. Growth processes
(DLA), rupture, earthquake and financial crashes seem to be characterized by
oscillatory or bounded regular microscopic functions g(x) that lead to a slow
power law decay of A(n), giving strong log-periodic amplitudes. In contrast,
the regular function g(x) of statistical physics models with
``ferromagnetic''-type interactions at equibrium involves unbound logarithms of
polynomials of the control variable that lead to a fast exponential decay of
A(n) giving weak log-periodic amplitudes and smoothed observables. These two
classes of behavior can be traced back to the existence or abscence of
``antiferromagnetic'' or ``dipolar''-type interactions which, when present,
make the Green functions non-monotonous oscillatory and favor spatial modulated
patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new
demonstration of the source of strong log-periodicity and of a justification
of the general offered classification, update of reference lis
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