9 research outputs found
Universal features of correlated bursty behaviour
Inhomogeneous temporal processes, like those appearing in human
communications, neuron spike trains, and seismic signals, consist of
high-activity bursty intervals alternating with long low-activity periods. In
recent studies such bursty behavior has been characterized by a fat-tailed
inter-event time distribution, while temporal correlations were measured by the
autocorrelation function. However, these characteristic functions are not
capable to fully characterize temporally correlated heterogenous behavior. Here
we show that the distribution of the number of events in a bursty period serves
as a good indicator of the dependencies, leading to the universal observation
of power-law distribution in a broad class of phenomena. We find that the
correlations in these quite different systems can be commonly interpreted by
memory effects and described by a simple phenomenological model, which displays
temporal behavior qualitatively similar to that in real systems
Kosterlitz-Thouless-like deconfinement mechanism in the 2+1 dimensional Abelian Higgs model
We point out that the permanent confinement in a compact 2+1-dimensional U(1)
Abelian Higgs model is destroyed by matter fields in the fundamental
representation. The deconfinement transition is Kosterlitz-Thouless like. The
dual theory is shown to describe a three-dimensional gas of point charges with
logarithmic interactions which arises from an anomalous dimension of the gauge
field caused by critical matter field fluctuations. The theory is equivalent to
a sine-Gordon-like theory in 2+1 dimensions with an anomalous gradient energy
proportional to . The Callan-Symanzik equation is used to demonstrate that
this theory has a massless and a massive phase. The renormalization group
equations for the fugacity and stiffness parameter of the theory
show that the renormalization of induces an anomalous scaling dimension
of . The stiffness parameter of the theory has a universal jump
at the transition determined by the dimensionality and . As a byproduct
of our analysis, we relate the critical coupling of the sine-Gordon-like theory
to an {\it a priori} arbitrary constant that enters into the computation of
critical exponents in the Abelian Higgs model at the charged infrared-stable
fixed point of the theory, enabling a determination of this parameter. This
facilitates the computation of the critical exponent at the charged fixed
point in excellent agreement with one-loop renormalization group calculations
for the three-dimensional XY-model, thus confirming expectations based on
duality transformations.Comment: 42 pages, no figures; v2: typos corrected, references updated;
version in press in Nucl. Phys.