20,769 research outputs found
Jordan weak amenability and orthogonal forms on JB*-algebras
We prove the existence of a linear isometric correspondence between the
Banach space of all symmetric orthogonal forms on a JB-algebra
and the Banach space of all purely Jordan generalized derivations
from into . We also establish the existence of a
similar linear isometric correspondence between the Banach spaces of all
anti-symmetric orthogonal forms on , and of all Lie Jordan
derivations from into
Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems
We investigate a 1D disordered Hamiltonian with a non analytical step-like
dispersion relation whose level statistics is exactly described by Semi-Poisson
statistics(SP). It is shown that this result is robust, namely, does not depend
neither on the microscopic details of the potential nor on a magnetic flux but
only on the type of non-analyticity. We also argue that a deterministic kicked
rotator with a non-analytical step-like potential has the same spectral
properties. Semi-Poisson statistics (SP), typical of pseudo-integrable
billiards, has been frequently claimed to describe critical statistics, namely,
the level statistics of a disordered system at the Anderson transition (AT).
However we provide convincing evidence they are indeed different: each of them
has its origin in a different type of classical singularities.Comment: typos corrected, 4 pages, 3 figure
A semiclassical theory of the Anderson transition
We study analytically the metal-insulator transition in a disordered
conductor by combining the self-consistent theory of localization with the one
parameter scaling theory. We provide explicit expressions of the critical
exponents and the critical disorder as a function of the spatial
dimensionality, . The critical exponent controlling the divergence of
the localization length at the transition is found to be . This result confirms that the upper critical dimension is
infinity. Level statistics are investigated in detail. We show that the two
level correlation function decays exponentially and the number variance is
linear with a slope which is an increasing function of the spatial
dimensionality.Comment: 4 pages, journal versio
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