In this article, we study the short-and long-range perturbations of periodic Schrr odinger operators. The asymptotic completeness is proved in the short-range case by referring to known results on the stationary approach and more explicitly with the time-dependent approach. In the long-range case, one is able to construct modiied wave operators. In both cases, the asymptotic observables can be ...

We revisit the old problem of nding the stability and instability intervals of a secondorder elliptic equation on the real line with periodic coe cients (Hill’s equation). It is well known that the stability intervals correspond to the spectrum of the Bloch family of operators de ned on a single period. Here we propose a characterization of the instability intervals. We introduce a new family o...

The Wigner-Kirkwood h-expansion of theWigner transform of the Bloch density can be resummed in the case of non local potentials if we keep only up to second order derivatives of the Wigner transform of the non-local potential with respect to the phase space variables. We also investigate a second approximation to the Bloch density where care has been taken with respect to a consistent h expansi...

A kind of tunable hyperbolic metamaterial (HMM) based on the graphene-dielectric layered structure at near-infrared frequencies is presented, and the engineered surface Bloch waves between graphene-based HMM and isotropic medium are investigated. Our calculations demonstrate that the frequency and frequency range of surface Bloch waves existence can be tuned by varying the Fermi energy of graph...

We report experimental observation of intrinsic Bloch-mode emission from a 3D tungsten photonic crystal at low thermal excitation. After the successful removal of conventional metallic emission (normal emission), it is possible to make an accurate comparison of the Bloch-mode and the normal emission. For all biases, we found that the emission intensity of the Bloch-mode is higher than that of t...

In this paper, surface waves in the presence of an infinite periodic array of obstacles of rectangular cross-section are considered. Rayleigh–Bloch surface waves are described by a localised wave motion which does not propagate energy away from the array. The periodicity of the array implies the existence of a cut-off frequency below which Rayleigh–Bloch surface waves may be sought. Such soluti...

The review considers the influence of Bloch surface waves on the optical and magneto-optical effects observed in photonic crystals; for example, the Goos–Hänchen effect, the Faraday effect, optical trapping and so on. Prospects for using Bloch surface waves for spatial light modulation, for controlling the polarization of light, for optical trapping and control of micro-objects are discussed.

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

We use polarization operators known from quantum theory of angular momentum to expand the N ×N dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties and derive positivity conditions for any N. We also apply the procedure to study Bloch vector space for a qubit and a qutrit.

The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. Theoretical analysis and some examples show that the proposed criteria can be more efficient than the previous rela...