Lévy's stochastic area in stochastic mechanics

Using the methods of Hida's white noise calculus, we study Lévy's stochastic area spanned by a two-dimensional stochastic process of relevance in Nelson's stochastic mechanics. An intriguing partial relationship is found with quantum mechanical angular momentum for the associated Schrödinger wave-function.     

Groups whose Proper Subgroups of Infinite Rank Have a Transitive Normality Relation

A group G is called a T-group if all its subnormal subgroups are normal, and G is a ${\bar{T}}$ -group if every subgroup of G has the property T. It is proved here that if G is a locally soluble group whose proper subgroups of infinite rank have the T-property, then either G is a ${\bar{T}}$ -group or it has finite rank.     

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of C. A. Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)]] who has recently observed this crossover temperature.     

Random fields on Riemannian manifolds: A constructive approach

We extend to Euclidean fields on a wide class of Riemannian manifolds two results which have proven to be crucial in the construction of interacting quantum fields in the flat case, namely local regularity properties of the free covariance in two dimensions and Osterwalder-Schrader positivity.Work supported in part by Ministero della Pubblica Istruzione     

Association of Molybdenum Ionic Species with Alumina Surface

The adsorption isotherms at 25, 45, and 65 degrees C of molybdenum solutions of concentration ranges between 10(-3) and 3x10(-2) M(Mo) (pH 4-5) on different alumina samples are investigated. The analysis is conducted using a modified Frumkin isotherm which takes a more realistic account of the lateral interaction between adsorbed species and considers that the adsorption takes place on the most basic OH groups on the surface of alumina. The results are discussed in view of the difference in solutions speciation, and the changes in the pH of the remaining supernatant solutions. The solution temperature, PZC of the used aluminas, the configuration of the basic OH groups on their surface, and the pore structure have been shown to intervene effectively. Copyright 2000 Academic Press.     

Evidence for radial flow of thermal dileptons in high-energy nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass dimuon production in 158A GeV In-In collisions. An excess of pairs above the known meson decays has been reported before. We now present precision results on the associated transverse momentum spectra. The slope parameter Teff extracted from the spectra rises with dimuon mass up to the rho, followed by a sudden decline above. While the initial rise is consistent with the expectations for radial flow of a hadronic decay source, the decline signals a transition to an emission source with much smaller flow. This may well represent the first direct evidence for thermal radiation of partonic origin in nuclear collisions.     

Perturbation of Transmission Matrices in Nonlinear Random Media

Random media with tailored optical properties are attracting burgeoning interest for applications in imaging, biophysics, energy, nanomedicine, spectroscopy, cryptography, and telecommunications. A key paradigm for devices based on this class of materials is the transmission matrix, the tensorial link between the input and the output signals, that describes in full their optical behavior. The transmission matrix has specific statistical properties, such as the existence of lossless channels, that can be used to transmit information, and are determined by the disorder distribution. In nonlinear materials, these channels may be modulated and the transmission matrix tuned accordingly. Here, the direct measurement of the nonlinear transmission matrix of complex materials is reported, exploiting the strong optothermal nonlinearity of scattering silica aerogel (SA). It is shown that the dephasing effects due to nonlinearity are both controllable and reversible, opening the road to applications based on the nonlinear response of random media.     

Weakly power automorphisms of groups

An automorphism α of a group G is called a weakly power automorphism if it maps every non-periodic subgroup of G onto itself. The aim of this paper is to investigate the behavior of weakly power automorphisms. In particular, among other results, it is proved that all weakly power automorphisms of a soluble non-periodic group G of derived length at most 3 are power automorphisms, i.e. they fix all subgroups of G. This result is best possible, as there exists a soluble non-periodic group of derived length 4 admitting a weakly power automorphism, which is not a power automorphism.