On the computation of a certain class of Hill determinants

AbstractHill's equation is studied for a particular class of periodic functions, which covers a broad range of practical applications. The essential quantity, which determines the stability criteria, is an infinite (or Hill) determinant. A set of recurrence relations for the computation of this determinant is derived. It is shown how these recurrence formulae also yield analytical results in two extremes

Cluster coherent potential approximation for electronic structure of disordered alloys

We extend the single-site coherent potential approximation (CPA) to include the effects of non-local disorder correlations (alloy short-range order) on the electronic structure of random alloy systems. This is achieved by mapping the original Anderson disorder problem to that of a selfconsistently embedded cluster. This cluster problem is then solved using the equations of motion technique. The CPA is recovered for cluster size $N_{c}=1$, and the disorder averaged density-of-states (DOS) is always positive definite. Various new features, compared to those observed in CPA, and related to repeated scattering on pairs of sites, reflecting the effect of SRO are clearly visible in the DOS. It is explicitly shown that the cluster-CPA method always yields positive-definite DOS. Anderson localization effects have been investigated within this approach. In general, we find that Anderson localization sets in before band splitting occurs, and that increasing partial order drives a continuous transition from an Anderson insulator to an incoherent metal.Comment: 7 pages, 6 figures. submitted to PR

An experimental study to discriminate between the validity of diffraction theories for off-Bragg replay

We show that experiments clearly verify the assumptions made by the first-order two-wave coupling theory for one dimensional lossless unslanted planar volume holographic gratings using the beta-value method rather than Kogelnik's K-vector closure method. Apart from the fact that the diffraction process is elastic, a much more striking difference between the theories becomes apparent particularly in the direction of the diffracted beam in off-Bragg replay. We therefore monitored the direction of the diffracted beam as a function of the off-Bragg replay angle in two distinct cases: [a] the diffracted beam lies in the plane of incidence and [b] the sample surface normal, the grating vector and the incoming beam do not form a plane which calls for the vectorial theory and results in conical scattering.Comment: Corrected Eqs. (3) & (6); 14 pages, 8 figure

Developments in the negative-U modelling of the cuprate HTSC systems

The paper deals with the many stands that go into creating the unique and complex nature of the HTSC cuprates above Tc as below. Like its predecessors it treats charge, not spin or lattice, as prime mover, but thus taken in the context of the chemical bonding relevant to these copper oxides. The crucial shell filling, negative-U, double-loading fluctuations possible there require accessing at high valent local environment as prevails within the mixed valent, inhomogeneous two sub-system circumstance of the HTSC materials. Close attention is paid to the recent results from Corson, Demsar, Li, Johnson, Norman, Varma, Gyorffy and colleagues.Comment: 44 pages:200+ references. Submitted to J.Phys.:Condensed Matter, Sept 7 200

Potentiel électrostatique d'une dislocation chargée

In this paper we show that the differential equation, giving the electrostatical potential of a dislocation at rest i.e. having around it a Debye-Huckel cloud of vacancies, can be integrated in a more rigorous manner by means of a Green's function method. We get for the potential a series having completely the character of a perturbation series. The convergence of this series is proved, for the most frequently occuring values of the parameters.Nous avons montré que l'équation différentielle du potentiel d'une dislocation en repos et autour de laquelle le nuage Debye-Huckel de lacunes est en équilibre peut être intégrée de façon rigoureuse, grâce à la théorie des fonctions de Green. Nous obtenons, pour le potentiel, une expression en forme de série, qui a complètement l'aspect d'une série de perturbations. A l'aide de la méthode des majorantes, il est possible de prouver la convergence de cette série dans la plupart des cas qui peuvent se présenter