39,302 research outputs found
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
Computability of the causal boundary by using isocausality
Recently, a new viewpoint on the classical c-boundary in Mathematical
Relativity has been developed, the relations of this boundary with the
conformal one and other classical boundaries have been analyzed, and its
computation in some classes of spacetimes, as the standard stationary ones, has
been carried out.
In the present paper, we consider the notion of isocausality given by
Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out
isocausal comparisons with standard stationary spacetimes. As a consequence,
the qualitative behavior of the c-boundary (at the three levels: point set,
chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the
inclusion of Figure
State selection in the noisy stabilized Kuramoto-Sivashinsky equation
In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with
additive uncorrelated stochastic noise. The Eckhaus stable band of the
deterministic equation collapses to a narrow region near the center of the
band. This is consistent with the behavior of the phase diffusion constants of
these states. Some connections to the phenomenon of state selection in driven
out of equilibrium systems are made.Comment: 8 pages, In version 3 we corrected minor/typo error
Anderson transition in a three dimensional kicked rotor
We investigate Anderson localization in a three dimensional (3d) kicked
rotor. By a finite size scaling analysis we have identified a mobility edge for
a certain value of the kicking strength . For dynamical
localization does not occur, all eigenstates are delocalized and the spectral
correlations are well described by Wigner-Dyson statistics. This can be
understood by mapping the kicked rotor problem onto a 3d Anderson model (AM)
where a band of metallic states exists for sufficiently weak disorder. Around
the critical region we have carried out a detailed study of the
level statistics and quantum diffusion. In agreement with the predictions of
the one parameter scaling theory (OPT) and with previous numerical simulations
of a 3d AM at the transition, the number variance is linear, level repulsion is
still observed and quantum diffusion is anomalous with . We note that in the 3d kicked rotor the dynamics is not random but
deterministic. In order to estimate the differences between these two
situations we have studied a 3d kicked rotor in which the kinetic term of the
associated evolution matrix is random. A detailed numerical comparison shows
that the differences between the two cases are relatively small. However in the
deterministic case only a small set of irrational periods was used. A
qualitative analysis of a much larger set suggests that the deviations between
the random and the deterministic kicked rotor can be important for certain
choices of periods. Contrary to intuition correlations in the deterministic
case can either suppress or enhance Anderson localization effects.Comment: 10 pages, 5 figure
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