46,771 research outputs found
Fractal von Neumann entropy
We consider the {\it fractal von Neumann entropy} associated with the {\it
fractal distribution function} and we obtain for some {\it universal classes h
of fractons} their entropies. We obtain also for each of these classes a {\it
fractal-deformed Heisenberg algebra}. This one takes into account the braid
group structure of these objects which live in two-dimensional multiply
connected space.Comment: latex, 9 pages, typos correcte
Fractal index, central charge and fractons
We introduce the notion of fractal index associated with the universal class
of particles or quasiparticles, termed fractons, which obey specific
fractal statistics. A connection between fractons and conformal field
theory(CFT)-quasiparticles is established taking into account the central
charge and the particle-hole duality
, for integer-value of the
statistical parameter. In this way, we derive the Fermi velocity in terms of
the central charge as . The Hausdorff dimension
which labelled the universal classes of particles and the conformal anomaly are
therefore related. Following another route, we also established a connection
between Rogers dilogarithm function, Farey series of rational numbers and the
Hausdorff dimension.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000
A quantum-geometrical description of fracton statistics
We consider the fractal characteristic of the quantum mechanical paths and we
obtain for any universal class of fractons labeled by the Hausdorff dimension
defined within the interval 1, a fractal
distribution function associated with a fractal von Neumann entropy. Fractons
are charge-flux systems defined in two-dimensional multiply connected space and
they carry rational or irrational values of spin. This formulation can be
considered in the context of the fractional quantum Hall effect-FQHE and number
theory.Comment: Typos corrected, latex, 8 pages, Talk given at the 2nd International
Londrina Winter School: Mathematical Methods in Physics, August, 26-30
(2002), Universidade Estadual de Londrina, Paran\'a, Brazil. Version to be
published in Int. J. Mod. Phys. {\bf A}, (2003
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