We report an experimental study of the Wannier-Stark fan and the fractional Wannier-Stark ladder using laser-cooled sodium atoms in an accelerating one-dimensional standing wave of light. We prepare the atoms in the lowest motional band of the optical lattice and then impose a constant acceleration. A weak oscillatory component is added to the acceleration in order to resonantly drive interband...

Recall first that a weight k Hodge structure (L,L) has coniveau c ≤ k2 if the Hodge decomposition of LC takes the form LC = Lk−c,c ⊕ Lk−c−1,c+1 ⊕ . . .⊕ Lc,k−c with Lk−c,c 6= 0. If X is a smooth complex projective variety and Y ⊂ X is a closed algebraic subset of codimension c, then Ker (H(X,Q) → H(X \ Y,Q)) is a sub-Hodge structure of coniveau ≥ c of H(X,Q) (cf. [32, Theorem 7]). The generaliz...

This paper connects the vanishing at the central critical value of the Lfunctions of certain polarized regular motives with the positivity of the rank of the associated p-adic (Bloch-Kato) Selmer groups. For the motives studied it is shown that vanishing of the L-value implies positivity of the rank of the Selmer group. It is further shown that if the the order of vanishing is positive and even...

By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass. §

The motion of charge particles in a superlattice structure subject to the crossed magnetic and electric fields, both applied in the in-plane direction, is discussed with respect to the novel type of terahertz oscillations suggested recently, [M. Orlita, R. Grill, L. Smrčka, M. Zvára, Phys. Rev. B 74 (2006) 125312]. The effects of the finite size of the superlattice is considered in comparison w...

We propose to use periodically spaced, curved optical waveguides for observation of optical Bloch oscillations. The refractive index distribution in this system is equivalent to the sum of a periodic term resulting from the equal spacing of the waveguides and a linear ramp, created by the curvature. We demonstrate numerically that light propagation in this geometry exhibits spatial Bloch oscill...

1 This is written for the volume Group formation in economics: networks, clubs, and coalitions edited by Gabrielle Demange and Myrna Wooders. This chapter is not intended to be a survey, and is quite naturally influenced by my own work. thank Francis Bloch and Myrna Wooders for helpful remarks.

m-Qubit states are embedded in Cl2m Clifford algebra. Their probability spectrum then depends on O (2m)or O (2m+ 1)-invariants respectively. Parameter domains for O (2m (+1))-vector and -tensor configurations, generalizing the notion of a Bloch sphere, are derived.

Despite the considerable progress in motivic cohomology and motivic homotopy theory achieved in recent years we still do not have a simple construction of the spectral sequence relating motivic cohomology and algebraic K-theory. The construction invented by Dan Grayson (see [3]) is simple and elegant but we are still unable to identify the E2-term of the resulting spectral sequence with the mot...

We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into and out of the lead. In the case of an infinitely extended interface we establish the relationship between these eigenfunctions and the Bloch states evaluate...