15 research outputs found
Pion Fluctuations near the QCD Critical Point
A critical point of second order, belonging to the universality class of the
3d Ising model, has recently been advocated as a strong candidate for the
critical behaviour (at high temperatures) of QCD with non-zero quark masses.
The implications of this conjecture are investigated in the multiparticle
environment of high-energy collisions. A universal intermittency pattern of
pion-density fluctuations is found, at the critical point, and its association
to the critical exponents is discussed. A Monte Carlo simulation of critical
events, in heavy-ion collisions, reveals the detailed structure of these
fluctuations, suggesting a framework of (event-by-event) measurements in which
the critical theory of QCD may become falsifiable.Comment: 8 pages, 3 figures (ps
The Earth as a living planet: human-type diseases in the earthquake preparation process
The new field of complex systems supports the view that a number of systems
arising from disciplines as diverse as physics, biology, engineering, and
economics may have certain quantitative features that are intriguingly similar.
The earth is a living planet where many complex systems run perfectly without
stopping at all. The earthquake generation is a fundamental sign that the earth
is a living planet. Recently, analyses have shown that human-brain-type disease
appears during the earthquake generation process. Herein, we show that
human-heart-type disease appears during the earthquake preparation of the
earthquake process. The investigation is mainly attempted by means of critical
phenomena, which have been proposed as the likely paradigm to explain the
origins of both heart electric fluctuations and fracture induced
electromagnetic fluctuations. We show that a time window of the damage
evolution within the heterogeneous Earth's crust and the healthy heart's
electrical action present the characteristic features of the critical point of
a thermal second order phase transition. A dramatic breakdown of critical
characteristics appears in the tail of the fracture process of heterogeneous
system and the injury heart's electrical action. Analyses by means of Hurst
exponent and wavelet decomposition further support the hypothesis that a
dynamical analogy exists between the geological and biological systems under
study
Tsallis and Levy statistics in the preparation of an earthquake
International audiencePrecursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are distributed along the activated fault and sustain the system. (ii) The initial MHz part is thought to be due to the fracture of highly heterogeneous system that surrounds the family of asperities. Interestingly, the MHz EM time-series can be described in analogy with a thermal second order phase transition. Herein we focus on the MHz pre-seismic activity, and especially on the naturally arising question: what is the physical mechanism that organizes the heterogeneous system in its critical state? Combining ideas of Levy and Tsallis statistics and criticality with features hidden in the precursory MHz time-series we argue that a Levy walk type mechanism can organize the heterogeneous system to criticality. Based on a numerically produced truncated Levy walk, we propose a way to estimate in the stage of critical fluctuations: (i) the associated Levy index-a, which describes quantitatively the underlying Levy dynamics, and (ii) the range of values where the nonextesitive Tsallis index q is restricted. We also show that the kHz EM activity could not be described by a truncated Levy mechanism. This result further indicates an abrupt sweep of the population of asperities that sustain the system
Abrupt transition in a sandpile model
We present a fixed energy sandpile (FES) model which, by increasing the
initial energy,undergoes, at the level of individual configurations, a
discontinuous transition.The model is obtained by modifying the toppling
procedure in the BTW rules: the energy transfer from a toppling site takes
place only to neighbouring sites with less energy (negative gradient
constraint) and with a time ordering (asynchronous). The model is minimal in
the sense that removing either of the two above mentioned constraints (negative
gradient or time ordering) the abrupt transition goes over to a continuous
transition as in the usual BTW case. Therefore the proposed model offers an
unique possibility to explore at the microscopic level the basic mechanisms
underlying discontinuous transitions.Comment: 7 pages, 5 figure
Intermittency at critical transitions and aging dynamics at edge of chaos
We recall that, at both the intermittency transitions and at the Feigenbaum
attractor in unimodal maps of non-linearity of order , the dynamics
rigorously obeys the Tsallis statistics. We account for the -indices and the
generalized Lyapunov coefficients that characterize the
universality classes of the pitchfork and tangent bifurcations. We identify the
Mori singularities in the Lyapunov spectrum at the edge of chaos with the
appearance of a special value for the entropic index . The physical area of
the Tsallis statistics is further probed by considering the dynamics near
criticality and glass formation in thermal systems. In both cases a close
connection is made with states in unimodal maps with vanishing Lyapunov
coefficients.Comment: Proceedings of: STATPHYS 2004 - 22nd IUPAP International Conference
on Statistical Physics, National Science Seminar Complex, Indian Institute of
Science, Bangalore, 4-9 July 2004. Pramana, in pres
Fractals at T=Tc due to instanton-like configurations
We investigate the geometry of the critical fluctuations for a general system
undergoing a thermal second order phase transition. Adopting a generalized
effective action for the local description of the fluctuations of the order
parameter at the critical point () we show that instanton-like
configurations, corresponding to the minima of the effective action functional,
build up clusters with fractal geometry characterizing locally the critical
fluctuations. The connection between the corresponding (local) fractal
dimension and the critical exponents is derived. Possible extension of the
local geometry of the system to a global picture is also discussed.Comment: To appear in Physical Review Letter
The Fractal Geometry of Critical Systems
We investigate the geometry of a critical system undergoing a second order
thermal phase transition. Using a local description for the dynamics
characterizing the system at the critical point T=Tc, we reveal the formation
of clusters with fractal geometry, where the term cluster is used to describe
regions with a nonvanishing value of the order parameter. We show that,
treating the cluster as an open subsystem of the entire system, new
instanton-like configurations dominate the statistical mechanics of the
cluster. We study the dependence of the resulting fractal dimension on the
embedding dimension and the scaling properties (isothermal critical exponent)
of the system. Taking into account the finite size effects we are able to
calculate the size of the critical cluster in terms of the total size of the
system, the critical temperature and the effective coupling of the long
wavelength interaction at the critical point. We also show that the size of the
cluster has to be identified with the correlation length at criticality.
Finally, within the framework of the mean field approximation, we extend our
local considerations to obtain a global description of the system.Comment: 1 LaTeX file, 4 figures in ps-files. Accepted for publication in
Physical Review