Diffusion Processes and Coherent States

It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum mechanics, the harmonic-oscillator coherent and squeezed states. The method allows to derive new minimum uncertainty states in time-dependent oscillator potentials and for the Caldirola-Kanai model of quantum damped oscillator.Comment: 11 pages, plain LaTe

Quaternions and Special Relativity

We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity.Comment: 17 pages, latex, no figure

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz

Testing Modified Newtonian Dynamics with Low Surface Brightness Galaxies --Rotation curve fits-

We present MOND (Modified Newtonian Dynamics) fits to 15 rotation curves of LSB galaxies. Good fits are readily found, although for a few galaxies minor adjustments to the inclination are needed. Reasonable values for the stellar mass-to-light ratios are found, as well as an approximately constant value for the total (gas and stars) mass-to-light ratio. We show that the LSB galaxies investigated here lie on the one, unique Tully-Fisher relation, as predicted by MOND. The scatter on the Tully-Fisher relation can be completely explained by the observed scatter in the total mass-to-light ratio. We address the question of whether MOND can fit any arbitrary rotation curve by constructing a plausible fake model galaxy. While MOND is unable to fit this hypothetical galaxy, a normal dark halo fit is readily found, showing that dark matter fits are much less selective in producing fits. The good fits to rotation curves of LSB galaxies support MOND, especially as these are galaxies with large mass discrepancies deep in the MOND regime.Comment: Accepted for publication in Astrophysical Journal 14 page

On the interface polaron formation in organic field-effect transistors

A model describing the low density carrier state in an organic single crystal FET with high-$\kappa$ gate dielectrics is studied. The interplay between charge carrier coupling with inter-molecular vibrations in the bulk of the organic material and the long-range interaction induced at the interface with a polar dielectric is investigated. This interplay is responsible for the stabilization of a polaronic state with an internal structure extending on few lattice sites, at much lower coupling strengths than expected from the polar interaction alone. This effect could give rise to polaron self-trapping in high-$\kappa$ organic FET's without invoking unphysically large values of the carrier interface interaction.Comment: 9 pages, 9 figure

Paired composite fermion wavefunctions

We construct a family of BCS paired composite fermion wavefunctions that generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions the groundstate can be very accurately represented in this form.Comment: 4 pages, 2 figure

Charge, Orbital and Magnetic Order in Nd0.5Ca0.5MnO3

In the manganite Nd0.5Ca0.5MnO3, charge ordering occurs at much higher temperature than the antiferromagnetic order (TCO=250K,TN=160K). The magnetic behavior of the phase TN<T<TCO is puzzling: its magnetization and susceptibility are typical of an antiferromagnet while no magnetic order is detected by neutron diffraction.We have undertaken an extensive study of the cristallographic, electric and magnetic properties of Nd0.5Ca0.5MnO3 and established its phase diagram as a function of temperature and magnetic field. The charge disordered, paramagnetic phase above TCO present ferromagnetic correlations. An antiferromagnetic CE phase prevails below TN, with complete charge and orbital ordering. In the intermediate temperature range, charge ordering occurs while orbital ordering sets in progressively, with no magnetic order. Strong magnetic fields destroy the charge ordered phases in a fisrt order transition towards a ferromagnetic state.Comment: 17 pages, 11 Figures to appear in Phys. Rev.