267 research outputs found
Nonextensive statistical mechanics - Applications to nuclear and high energy physics
A variety of phenomena in nuclear and high energy physics seemingly do not
satisfy the basic hypothesis for possible stationary states to be of the type
covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the
system appears to relax, along time, on macroscopic states which violate the
ergodic assumption. Some of these phenomena appear to follow, instead, the
prescriptions of nonextensive statistical mechanics. In the same manner that
the BG formalism is based on the entropy , the
nonextensive one is based on the form (with
). Typically, the systems following the rules derived from the
former exhibit an {\it exponential} relaxation with time toward a stationary
state characterized by an {\it exponential} dependence on the energy ({\it
thermal equilibrium}), whereas those following the rules derived from the
latter are characterized by (asymptotic) {\it power-laws} (both the typical
time dependences, and the energy distribution at the stationary state). A brief
review of this theory is given here, as well as of some of its applications,
such as electron-positron annihilation producing hadronic jets, collisions
involving heavy nuclei, the solar neutrino problem, anomalous diffusion of a
quark in a quark-gluon plasma, and flux of cosmic rays on Earth. In addition to
these points, very recent developments generalizing nonextensive statistical
mechanics itself are mentioned.Comment: 23 pages including 5 figures. To appear in the Proceedings of the Xth
International Workshop on Multiparticle Production - Correlations and
Fluctuations in QCD (8-15 June 2002, Crete), ed. N. Antoniou (World
Scientific, Singapore, 2003). It includes a reply to the criticism expressed
in R. Luzzi, A.R. Vasconcellos and J.G. Ramos, Science 298, 1171 (2002
G\"odel-type Spacetimes in Induced Matter Gravity Theory
A five-dimensional (5D) generalized G\"odel-type manifolds are examined in
the light of the equivalence problem techniques, as formulated by Cartan. The
necessary and sufficient conditions for local homogeneity of these 5D manifolds
are derived. The local equivalence of these homogeneous Riemannian manifolds is
studied. It is found that they are characterized by three essential parameters
, and : identical triads correspond to
locally equivalent 5D manifolds. An irreducible set of isometrically
nonequivalent 5D locally homogeneous Riemannian generalized G\"odel-type
metrics are exhibited. A classification of these manifolds based on the
essential parameters is presented, and the Killing vector fields as well as the
corresponding Lie algebra of each class are determined. It is shown that the
generalized G\"odel-type 5D manifolds admit maximal group of isometry
with , or depending on the essential parameters ,
and . The breakdown of causality in all these classes of homogeneous
G\"odel-type manifolds are also examined. It is found that in three out of the
six irreducible classes the causality can be violated. The unique generalized
G\"odel-type solution of the induced matter (IM) field equations is found. The
question as to whether the induced matter version of general relativity is an
effective therapy for these type of causal anomalies of general relativity is
also discussed in connection with a recent article by Romero, Tavakol and
Zalaletdinov.Comment: 19 pages, Latex, no figures. To Appear in J.Math.Phys.(1999
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