Linear perturbations of the Wigner transform and the Weyl quantization

We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner transform, but in general they do not belong to Cohen's class. We provide a characterization of the intersection of the two classes. To any such time-frequency representation, we associate a pseudodifferential calculus. We investigate the related quantization procedure, study the properties of the pseudodifferential operators, and compare the formalism with that of the Weyl calculus.Comment: 38 pages. Contributed chapter for volume on the occasion of Luigi Rodino's 70th birthda

Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Octahedral tilting, monoclinic phase and the phase diagram of PZT

Anelastic and dielectric spectroscopy measurements on PZT close to the morphotropic (MPB) and antiferroelectric boundaries provide new insight in some controversial aspects of its phase diagram. No evidence is found of a border separating monoclinic (M) from rhombohedral (R) phases, in agreement with recent structural studies supporting a coexistence of the two phases over a broad composition range x < 0.5, with the fraction of M increasing toward the MPB. It is also discussed why the observed maximum of elastic compliance appears to be due to a rotational instability of the polarisation and therefore cannot be explained by extrinsic softening from finely twinned R phase alone, but indicates the presence also of M phase, not necessarily homogeneous. A new diffuse transition is found within the ferroelectric phase near x ~ 0.1, at a temperature T_IT higher than the well established boundary T_T to the phase with tilted octahedra. It is proposed that around T_IT the octahedra start rotating in a disordered manner and finally become ordered below T_T. In this interpretation, the onset temperature for octahedral tilting monotonically increases up to the antiferroelectric transition of PbZrO3, and the depression of T_T(x) below x = 0.18 would be a consequence of the partial relieve of the mismatch between the cation radii with the initial stage of tilting below T_IT.Comment: submitted to J. Phys.: Condens. Matte

Low-temperature phase transformations of PZT in the morphotropic phase-boundary region

We present anelastic and dielectric spectroscopy measurements of PbZr(1-x)Ti(x)O(3) with 0.455 < x < 0.53, which provide new information on the low temperature phase transitions. The tetragonal-to-monoclinic transformation is first-order for x < 0.48 and causes a softening of the polycrystal Young's modulus whose amplitude may exceed the one at the cubic-to-tetragonal transformation; this is explainable in terms of linear coupling between shear strain components and tilting angle of polarization in the monoclinic phase. The transition involving rotations of the octahedra below 200 K is visible both in the dielectric and anelastic losses, and it extends within the tetragonal phase, as predicted by recent first-principle calculations.Comment: 4 pages, 4 figure

Thermal convection in fluidized granular systems

Thermal convection is observed in molecular dynamic simulation of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a rectangular box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The observed convection comes from the effect of gravity and the spontaneous granular temperature gradient that the system dynamically develops.Comment: 4 pages, 5 figure

The Degenerate Parametric Oscillator and Ince's Equation

We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their connections with dynamical invariants and SU(1,1) group are also discussed.Comment: 10 pages, no figure

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

Effect of Structural Parameters on Superconductivity in Fluorine-Free LnFeAsO1-y (Ln=La,Nd)

The crystal structure of LnFeAsO$_{1-y}$ (Ln = La, Nd) has been studied by the powder neutron diffraction technique. The superconducting phase diagram of NdFeAsO$_{1-y}$ is established as a function of oxygen content which is determined by Rietveld refinement. The small As-Fe bond length suggests that As and Fe atoms are connected covalently. FeAs$_4$-tetrahedrons transform toward a regular shape with increasing oxygen deficiency. Superconducting transition temperatures seem to attain maximum values for regular FeAs$_4$-tetrahedrons

Multiplication and Composition in Weighted Modulation Spaces

We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer look onto associated norm inequalities under restrictions in the Fourier image. This will give us the opportunity to treat the boundedness of composition operators.Comment: 49 page

On scattering off the extreme Reissner-Nordstr\"om black hole in N=2 supergravity

The scattering amplitudes for the perturbed fields of the N=2 supergravity about the extreme Reissner-Nordstr\"om black hole is examined. Owing to the fact that the extreme hole is a BPS state of the theory and preserves an unbroken global supersymmetry(N=1), the scattering amplitudes of the component fields should be related to each other. In this paper, we derive the formula of the transformation of the scattering amplitudes.Comment: 9 pages, revtex, no figures, a few typing errors correcte