Scattering Theory Approach to Random Schroedinger Operators in One Dimension

Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the scattering phase by the theorem of Birman and Krein. The spectral shift density is defined as the "thermodynamic limit" of the spectral shift function per unit length of the interaction region. This density is shown to be equal to the difference of the densities of states for the free and the interacting Hamiltonians. Based on this construction, we give a new proof of the Thouless formula. We provide a prescription how to obtain the Lyapunov exponent from the scattering matrix, which suggest a way how to extend this notion to the higher dimensional case. This prescription also allows a characterization of those energies which have vanishing Lyapunov exponent.Comment: 1 figur

Experimental study of Taylor's hypothesis in a turbulent soap film

An experimental study of Taylor's hypothesis in a quasi-two-dimensional turbulent soap film is presented. A two probe laser Doppler velocimeter enables a non-intrusive simultaneous measurement of the velocity at spatially separated points. The breakdown of Taylor's hypothesis is quantified using the cross correlation between two points displaced in both space and time; correlation is better than 90% for scales less than the integral scale. A quantitative study of the decorrelation beyond the integral scale is presented, including an analysis of the failure of Taylor's hypothesis using techniques from predictability studies of turbulent flows. Our results are compared with similar studies of 3D turbulence.Comment: 27 pages, + 19 figure

Transcriptomic characterization of bud dormancy in apple.

Resumo

Volume and diagnosis: an approach to cross-border care in eight European countries

Objectives: Mobility of patients is a pertinent issue on the European Union's agenda. This study aimed to estimate the volume and main diagnoses of cross-border care in eight European countries, in order to provide policy makers with background information about the nature of patient mobility in Europe. Methods: This article reports the combined findings from three independent studies that compiled self-reported information on admissions data and main diagnoses from more than 200 hospitals in eight European countries. Results: The average volume of cross-border patients accounted for less than 1% of total admissions in the hospitals studied here. Diseases of the circulatory system (mainly acute myocardial infarction) and fractures were the most common reasons for hospitalisation of European patients abroad. Deliveries and other diagnoses related to pregnancy, pneumonia, appendicitis and other diseases of the digestive system, aftercare procedures, and disorders of the eye and adnexa were also common diagnoses for this population. Conclusions: Hospitals should reinforce their efforts to adapt the care provided to the needs of foreign patients in treatment areas that cover the most frequent pathologies identified in this populatio

Transcription profiling of the chilling requirement for bud break in apples: a putative role for FLC-like genes.

doi:10.1093/jxb/erv0

Lifshitz Tails in Constant Magnetic Fields

We consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained in the case of a vanishing magnetic field