On the Density-Density Critical Indices¶in Interacting Fermi Systems

The behaviour of correlation functions of d=1$ interacting fermionic systems is determined by a small number of critical indices. We prove that one of them is exactly zero. As a consequence, the behavior of the Fourier transform of the density-density correlation at zero momentum is qualitatively unaffected by the interaction, contrary to what happens at , if is the Fermi momentum. The result is obtained by implementing Ward identities in a Renormalization Group approach. Received: 12 November 2001 / Accepted: 25 February 2002?Published online: 2 October 2002     

Links in a thickened surface

For a given two-dimensional surface μ, we studi invariants for oriented links in μ×[0,1] which generalize the two-variable HOMFLY polynomials when μ is the 2-disk. These invariants are connected to multiparameter quantum groups whose special properties are discussed. Si studiano gli invarianti dei nodi in spazi del tipo μ×[0,1], dove μ è una superficie. Questi invarianti generalizzano gli invarianti di HOMFLY.

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(Conferenza tenuta dal Prof. P. Cotta-Ramusino il 16 maggio 1991)     

Ward Identities and Vanishing of the Beta Function for d = 1 Interacting Fermi Systems

We give a self consistent and simplified proof of the (asymptotic) vanishing of the Beta function in d=1 interacting Fermi systems as a consequence of a few properties deduced from the exact solution of the Luttinger model. Moreover, since the vanishing of the Beta function is usually “proved” in the physical literature through heuristic arguments based on Ward identities, we briefly discuss here also the possibility of exploiting this idea in a rigorous approach, by using a suitable Dyson equation. We show that there are serious difficulties, related to the presence of corrections (for which we get careful bounds), which are usually neglected.     

2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

FLUORESCENCE OF Euglena gracilis PHOTORECEPTOR PIGMENT: AN in vivo MICROSPECTROFLUOROMETRIC STUDY

Abstract— The spectroscopic characterization of the photoreceptor pigment is one of the main questions in the study of the photosensory transduction chains in photomotile microorganisms. One of the possible techniques that can be used is in vivo microspectrofluorometry. By means of a tunable dye-laser microspectrofiuorometer developed by us, we have investigated some of the spectroscopic properties of the photoreceptor pigment of the green flagellate Euglena gracilis. The in vivo fluorescence excitation spectrum has been determined and the fluorescence quantum yield has been measured. The results show that flavins are indeed present in the paraflagellar body of E. gracilis and that their fluorescence quantum yield is much lower than that of a free flavin. An estimate of the order of magnitude of the rate constants for primary molecular reactions is tentatively given.