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, $d$. The critical exponent $\nu$ controlling the divergence of the localization length at the transition is found to be $\nu = {1 \over 2}+ {1 \over {d-2}}$. 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

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

Anderson transition in systems with chiral symmetry

Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry.Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references, final version as published in Phys. Rev.

Symmetry limit properties of a priori mixing amplitudes for non-leptonic and weak radiative decays of hyperons

We show that the so-called parity-conserving amplitudes predicted in the a priori mixing scheme for non-leptonic and weak radiative decays of hyperons vanish in the strong-flavor symmetry limit

Multi-sensor system using plastic optical fibers for intrinsically safe level measurements

A system for measuring liquid level in multiple tanks using optical fibe technology has been developed. Oil fiel service industry or any sector requiring liquid level measurements in flammabl atmospheres can be benefite from this intrinsically safe technology. The device used a single lens for the emitting and receiving fibe and it is based on amplitude variations as a function of the liquid distance and not in time of fligh or phase detection. Being the firs fiber-opti liquid level sensor with those characteristics for long ranges (>200 cm). A simple model to describe their behavior has been derived and tested on two prototypes. A Monte-Carlo method is used to fi the experimental data and obtain the model parameters. High accuracy between experimental data and fitte curve is obtained. The prototypes have a good linearity, better than 1.5% FS (full scale). Sensor heads are made of plastic optical fiber (POF) that are easy to handle, flexible and economical. They are excited by 650 nm lasers, housed in ST-connectors to obtain compact and rough prototypes. Optical multiplexing is used to increase the measuring safety area. Frequency division multiplexing is used to address each sensor head. A discussion about the influenc of tilts and aberrations is also included.Publicad

Betti numbers of the moduli space of rank 3 parabolic Higgs bundles

We compute the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and we study their variation with this parameter.Comment: 78 pages. Extended version. Added a section with the fixed determinant case. To appear in Memoirs of the AM