Parabolic bundles and representations of the fundamental group

Let X be as smooth complex projective variety with Neron-Severi group isomorphic to Z, and D an irreducible divisor with normal crossing singularities. Assume r is equal to 2 or 3. We prove that if the fundamental group of X doesn't have irreducible PU(r) representations, then the fundamental group of X-D doesn't have irreducible U(r) representations. The proof uses the non-existence of certain stable parabolic bundles. We also obtain a similar result for GL(2) when D is smooth and X is a complex surface.Comment: 13 pages, 1 figure, LaTeX2

Soliton attenuation and emergent hydrodynamics in fragile matter

Disordered packings of soft grains are fragile mechanical systems that loose rigidity upon lowering the external pressure towards zero. At zero pressure, we find that any infinitesimal strain-impulse propagates initially as a non-linear solitary wave progressively attenuated by disorder. We demonstrate that the particle fluctuations generated by the solitary-wave decay, can be viewed as a granular analogue of temperature. Their presence is manifested by two emergent macroscopic properties absent in the unperturbed granular packing: a finite pressure that scales with the injected energy (akin to a granular temperature) and an anomalous viscosity that arises even when the microscopic mechanisms of energy dissipation are negligible. Consistent with the interpretation of this state as a fluid-like thermalized state, the shear modulus remains zero. Further, we follow in detail the attenuation of the initial solitary wave identifying two distinct regimes : an initial exponential decay, followed by a longer power law decay and suggest simple models to explain these two regimes.Comment: 8 pages, 3 Figure

Large Shell Model Calculations for Calcium Isotopes: Spectral Statistics and Chaos

We perform large shell model calculations for Calcium isotopes in the full fp shell by using the realistic Kuo-Brown interaction. The Calcium isotopes are especially interesting because the nearest-neighbour spacing distribution P(s) of low-lying energy levels shows significant deviations from the predictions of the Gaussian Orthogonal Ensemble of random--matrix theory. This contrasts with other neighbouring nuclei which show fully chaotic spectral distributions. We study the chaotic behaviour as a function of the excitation energy. In addition, a clear signature of chaos suppression is obtained when the single-particle spacings are increased. In our opinion the relatively weak strength of the neutron-neutron interaction is unable to destroy the regular single-particle mean-field motion completely. In the neighbouring nuclei with both protons and neutrons in valence orbits, on the other hand, the stronger proton-neutron interaction would appear to be sufficient to destroy the regular mean-field motion.Comment: Latex, 7 pages, 2 postscript figures, to be published in the Proceedings 'Highlights of Modern Nuclear Structure', S. Agata sui due Golfi (italy), Ed. A. Covello (World Scientific

Spectral Statistics in Large Shell Model Calculations

The spectral statistics of low--lying states of $fp$ shell nuclei are studied by performing large shell--model calculations with a realistic nuclear interaction. For $Ca$ isotopes, we find deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.Comment: 9 pages, LaTex, 3 figures available upon request, to appear in Proceedings of the V International Spring Seminar on Nuclear Physics, Ed. by A. Covello (World Scientific