Stability of solitons in parity-time (PT )-symmetric periodic potentials (optical lattices) is analyzed in both oneand two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while sta...

Based on a novel application of an archimedean type pairing to the geometry and deformation theory of K3 surfaces, we construct a regulator indecomposable K1-class on a self-product of a K3 surface. In the Appendix, we explain how this pairing is a special instance of a general pairing on precycles in the equivalence relation defining Bloch’s higher Chow groups.

Patrik Wyss, Shaihan J Malik, Vincent O Boer, Johanna J Bluemink, Alexander Raaijmakers, Mustafa Cavusoglu, Peter Luijten, Johannes J Hoogduin, Giel Mens, and Anke Henning Institute for Biomedical Engineering, UZH and ETH Zurich, Zurich, Switzerland, Imaging Sciences and Biomedical Engineering, Kings College London, London, United Kingdom, University Medical Center Utrecht, Utrecht, Netherlands...

We give a characterization of lacunary series in the Bloch space of the unit ball in C in terms of Taylor coefficients. We also characterize Bloch functions whose Taylor coefficients are nonnegative. The corresponding problems for BMOA are discussed as well.

In this paper, we study algebraic and analytic properties of Fourier coefficients, expressed as q-series, of the so-called Bloch-Okounkov n-point function. We prove several results about these series and explain how they relate to Rogers’ false theta function. Then we obtain their full asymptotics, as τ → 0, and use this result to derive asymptotic properties of the coefficients in the q-expans...

We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called Qp spaces that have attracted much attention lately.

Suppose that ϕ(z) is an analytic self-map of the unit disk ∆. We consider the boundedness of the composition operator C ϕ from Bloch space Ꮾ into the spaces Q T (Q T ,0) defined by a nonnegative, nondecreasing function T (r) on 0 ≤ r < ∞. 1. Introduction. Let ∆ = {z : |z| < 1} be the unit disk of complex plane C and let H(∆) be the space of all analytic functions in ∆. For a ∈ ∆, Green's functi...

Peter Schauß1,∗, Marc Cheneau, Manuel Endres, Takeshi Fukuhara, Sebastian Hild, Ahmed Omran, Thomas Pohl, Christian Gross, Stefan Kuhr, and Immanuel Bloch Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany University of Strathclyde, Department of Physics, SUPA, Glasgow G4 0NG, UK and Ludwig-Maximilians-Universit...

Central to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. While the theory of static effective property calculations goes back about 60 years, progress in the actual calculation of dynamic effective properties for periodic composites has been made only very recently. Here we discuss th...