We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra ŝl2 on a Maxwell-Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show t...

Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially...

The most general form for symmetric modes of nonlinear discrete-symmetry systems with nonlinearity depending on the modulus of the field is presented. Vortex solutions are demonstrated to behave as Bloch modes characterized by an angular Bloch momentum associated to a periodic variable, periodicity being fixed by the order of discrete point-symmetry of the system. The concept of angular Bloch m...

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as studied recently in experiments for optically induced photonic lattices [Trompeter, Phys. Rev. Lett. 96, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in the generic case of a Bragg reflection when the Bloch index crosses the edge of the irreduc...

We investigate coherent Bloch oscillations in GaAs/AlxGa1-xAs superlattices with electronic miniband widths larger than the optical phonon energy. In these superlattices the Bloch frequency can be tuned into resonance with the optical phonon. Close to resonance a direct coupling of Bloch oscillations to LO phonons is observed which gives rise to the coherent excitation of LO phonons. The densit...

This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast εY -periodic conductivity. When the conductivity is bounded in L1 and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ε−2, the first Bloch eigenvalue converges as ε → 0 to a limit which preserves the second-order expansion w...

Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc verifying that sup|z|<1(1−|z|)||f ′(z)|| < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and 1(Y ) if the map ∑∞ n=0 xnz n → (Tn(xn))n defines a bounded linear operator from Bloch(X) into 1(Y )...

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

In this paper, the boundedness and compactness of weighted composition operators from analytic Morrey spaces into Bloch-type spaces and little Bloch-type spaces are studied.

In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a re...