Quantum chaos in one dimension?

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.Comment: 7 pages, 10 figures, minor correction, references extende

Universal statistics of wave functions in chaotic and disordered systems

We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and analytical results show that the distribution function of a generalized Riccati variable, defined as the ratio of components of eigenfunctions on basis states coupled by perturbation, is universal, and has the form of Lorentzian distribution.Comment: 6 Europhys pages, 2 Ps figures, new version to appear in Europhys. Let

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Consider, in the domain of outer communication of a Kerr-Newman black hole, a point (observation event) and a timelike curve (worldline of light source). Assume that the worldline of the source (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of the observation event, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic of (Morse) index k from the observation event to the worldline of the source, hence an observer at the observation event sees infinitely many images of the source. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in the domain of outer communication are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.Comment: 14 pages, 2 figures; REVTEX; submitted to J. Math. Phy

Some Unpleasant General Equilibrium Implications of Executive Incentive Compensation Contracts

We consider a simple variant of the standard real business cycle model in which shareholders hire a self-interested executive to manage the firm on their behalf. Delegation gives rise to a generic conflict of interest mediated by a convex (option-like) compensation contract which is able to align the interests of managers and their shareholders. With such a compensation contract, a given increase in the firm's output generated by an additional unit of physical investment results in a more than proportional increase in the manager's income. We find that incentive contracts of this form can easily result in an indeterminate general equilibrium, with business cycles driven by self-fulfilling fluctuations in the manager's expectations. These expectations are unrelated to fundamentals. Arbitrarily large fluctuations in macroeconomic variables may possibly result.

A novel LAMB2 gene mutation associated with a severe phenotype in a neonate with Pierson syndrome.

BACKGROUND: Pierson syndrome (PS) is a rare autosomal recessive disorder, caused by mutations in the laminin β2 (LAMB2) gene. It is characterized by congenital nephrotic syndrome, microcoria, and neurodevelopmental deficits. Several mutations with genotype-phenotype correlations have been reported, often with great clinical variability. We hereby report a novel homozygous nonsense mutation in the LAMB2 gene, associated with a severe phenotype presentation. CASE DIAGNOSIS: We describe a term male infant born from consanguineous parents. The mother previously lost three children in the neonatal period, secondary to undefined renal disease, had two spontaneous abortions, and gave birth to one healthy daughter. The index case presented at birth with bilateral microcoria, severe hypotonia, respiratory distress, and congenital nephrotic syndrome associated with anuria and severe renal failure requiring peritoneal dialysis. The patients' clinical follow-up was unfavorable, and the newborn died at 7 days of life, after withdrawal of life support. Genetic analysis revealed a homozygous nonsense mutation at position c.2890C>T causing a premature stop codon (p.R964*) in LAMB2 gene. CONCLUSION: We here describe a novel nonsense homozygous mutation in LAMB2 gene causing a severe neonatal presentation of Pierson syndrome. This new mutation expands the genotype-phenotype spectrum of this rare disease and confirms that truncating mutations might be associated with severe clinical features

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Caloric stimulation of ampullar receptors: a new method to produce mechanically-evoked responses in frog semicircular canals

A microthermistor positioned close to the exposed posterior semicircular canal in isolated labyrinth preparations of the frog was used to stimulate the sensory organ. Our results indicated that, depending on the position of the heater, the induced endolymphatic convection currents may result in either excitatory or inhibitory cupular deflections and thus in a modulation of ampullar receptor resting activity. Other possible thermal-dependent mechanisms, such as a direct action of the stimulus on vestibular sensors or endolymphatic volume changes, had, in the present experimental conditions, a minor role. Caloric stimulation could therefore represent a novel method to stimulate the semicircular canals 'in situ'

Local Spectral Density for a Periodically Driven System of Coupled Quantum States with Strong Imperfection in Unperturbed Energies

A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system is excited by an external periodic field, the temporal profile of which is close to monochromatic one. The shape of local spectral density is shown to be well described by the contour obtained from a relevant model of periodically driven two-states system with irreversible losses to an external thermal bath. The shape width and the inverse participation ratio are determined as functions both of the Rabi frequency and of parameters specifying the localization effect for our system in the absence of external field.Comment: 6 pages, 5 figures, submitted to Optics and Spectroscop