LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.Comment: 11 page

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

LEA polypeptide profiling of recalcitrant and orthodox legume seeds reveals ABI3-regulated LEA protein abundance linked to desiccation tolerance

In contrast to orthodox seeds that acquire desiccation tolerance during maturation, recalcitrant seeds are unable to survive drying. These desiccation-sensitive seeds constitute an interesting model for comparative analysis with phylogenetically close species that are desiccation tolerant. Considering the importance of LEA (late embryogenesis abundant) proteins as protective molecules both in drought and in desiccation tolerance, the heat-stable proteome was characterized in cotyledons of the legume Castanospermum australe and it was compared with that of the orthodox model legume Medicago truncatula. RNA sequencing identified transcripts of 16 homologues out of 17 LEA genes for which polypeptides are detected in M. truncatula seeds. It is shown that for 12 LEA genes, polypeptides were either absent or strongly reduced in C. australe cotyledons compared with M. truncatula seeds. Instead, osmotically responsive, non-seed-specific dehydrins accumulated to high levels in the recalcitrant cotyledons compared with orthodox seeds. Next, M. truncatula mutants of the ABSCISIC ACID INSENSITIVE3 (ABI3) gene were characterized. Mature Mtabi3 seeds were found to be desiccation sensitive when dried below a critical water content of 0.4g H2O g DW–1. Characterization of the LEA proteome of the Mtabi3 seeds revealed a subset of LEA proteins with severely reduced abundance that were also found to be reduced or absent in C. australe cotyledons. Transcripts of these genes were indeed shown to be ABI3 responsive. The results highlight those LEA proteins that are critical to desiccation tolerance and suggest that comparable regulatory pathways responsible for their accumulation are missing in both desiccation-sensitive genotypes, revealing new insights into the mechanistic basis of the recalcitrant trait in seeds

A new numerical approach to Anderson (de)localization

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with small disorder allows states that are dynamically delocalized with positive probability. This approach is based on a recent result by Abakumov-Liaw-Poltoratski which is rooted in the study of spectral behavior under rank-one perturbations, and states that every non-zero vector is almost surely cyclic for the singular part of the operator. The numerical work presented is rather simplistic compared to other numerical approaches in the field. Further, this method eliminates effects due to boundary conditions. While we carried out the numerical experiment almost exclusively in the case of the two dimensional discrete random Schroedinger operator, we include the setup for the general class of Anderson models called Anderson-type Hamiltonians. We track the location of the energy when a wave packet initially located at the origin is evolved according to the discrete random Schroedinger operator. This method does not provide new insight on the energy regimes for which diffusion occurs.Comment: 15 pages, 8 figure

Localization criteria for Anderson models on locally finite graphs

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on \ZZ^d. We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder

Constructive Fractional-Moment Criteria for Localization in Random Operators

We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.Comment: Announcement and summary of results whose proofs are given elsewhere. LaTex (10 pages), uses Elsevier "elsart" files (attached

Temporal profiling of the heat-stable proteome during late maturation of Medicago truncatula seeds identifies a restricted subset of late embryogenesis abundant proteins associated with longevity

Developing seeds accumulate late embryogenesis abundant (LEA) proteins, a family of intrinsically disordered and hydrophilic proteins that confer cellular protection upon stress. Many different LEA proteins exist in seeds, but their relative contribution to seed desiccation tolerance or longevity (duration of survival) is not yet investigated. To address this, a reference map of LEA proteins was established by proteomics on a hydrophilic protein fraction from mature Medicago truncatula seeds and identified 35 polypeptides encoded by 16 LEA genes. Spatial and temporal expression profiles of the LEA polypeptides were obtained during the long maturation phase during which desiccation tolerance and longevity are sequentially acquired until pod abscission and final maturation drying occurs. Five LEA polypeptides, representing 6% of the total LEA intensity, accumulated upon acquisition of desiccation tolerance. The gradual 30-fold increase in longevity correlated with the accumulation of four LEA polypeptides, representing 35% of LEA in mature seeds, and with two chaperone-related polypeptides. The majority of LEA polypeptides increased around pod abscission during final maturation drying. The differential accumulation profiles of the LEA polypeptides suggest different roles in seed physiology, with a small subset of LEA and other proteins with chaperone-like functions correlating with desiccation tolerance and longevity

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page