Generalized Hessian and External Approximations in Variational Problems of Second Order

We introduce a suitable notion of generalized Hessian and show that it can be used to construct approximations by means of piecewise linear functions to the solutions of variational problems of second order. An important guideline of our argument is taken from the theory of the Γ-convergence. The convergence of the method is proved for integral functionals whose integrand is convex in the Hessian and satisfies standard growth conditions.     

A systematic investigation of the role of material parameters in metastability of hydrogenated amorphous silicon

In this work, the role of structural, electronic and optical parameters of as-deposited amorphous silicon films in photoconductivity decay during light soaking was systematically investigated. Deposition temperature was varied in the range 130–270°C, in order to obtain samples with different structural, optical and electronic properties. As a result, two degradation regimes were identified. At short illumination times (within a few days in typical samples, and within a few hours in the low quality samples), the material showed different tendency to degradation depending on the content of the SiH bond clusters. At long illumination times, in all the light soaked samples the photoconductivity decay followed the t^−1/3 law. The measured photoconductivity degradation was simulated starting from the bond-breaking model. The observed correlation between the material structural parameters and the different tendencies to degradation is explained in terms of variations of the Staebler-Wronski susceptibility.     

Algebraic classification of ℂP n instanton solutions

The finite condition for two-dimensional ℂP ⁿ models is discussed noting that one can impose boundary conditions such that the domain of the field is a compact Riemann surface S _g. Holomorphic maps φ: S _g →ℂP ⁿ give finite energy solutions of the classical field equations, which are classified according to standard methods of algebraic geometry. The moduli problem is discussed in detail for S _g =ℂP ¹=S ².     

Spectral density method for an anisotropic linear chain

The spectral density method is used to study the thermodynamic properties of an anisotropic antiferromagnetic Heisenberg linear chain in an external magnetic field. Insecond order approximation without the decoupling procedure for the two particle correlation function, we are able to obtain many results in terms of both the temperature and the magnetic field for different values of the anisotropy parameter. The ground state of the model is investigated and the singular behaviour of some thermodynamic quantities near the critical field is determined. In particular, explicit analytical solutions are given for small anisotropy parameters. Our results are compared with the ones obtained by means of other methods and some exact results are reproduced.