Bloch electron in a magnetic field and the Ising model

The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.Comment: 4 pages, 1 figure, REVTE

Suppressed spin dephasing for 2D and bulk electrons in GaAs wires due to engineered cancellation of spin-orbit interaction terms

We report a study of suppressed spin dephasing for quasi-one-dimensional electron ensembles in wires etched into a GaAs/AlGaAs heterojunction system. Time-resolved Kerr-rotation measurements show a suppression that is most pronounced for wires along the [110] crystal direction. This is the fingerprint of a suppression that is enhanced due to a strong anisotropy in spin-orbit fields that can occur when the Rashba and Dresselhaus contributions are engineered to cancel each other. A surprising observation is that this mechanisms for suppressing spin dephasing is not only effective for electrons in the heterojunction quantum well, but also for electrons in a deeper bulk layer.Comment: 5 pages, 3 figure

Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.Comment: 12 pages, to appear in Commun. Math. Phy

Trachoma and Ocular Chlamydial Infection in the Era of Genomics.

Trachoma is a blinding disease usually caused by infection with Chlamydia trachomatis (Ct) serovars A, B, and C in the upper tarsal conjunctiva. Individuals in endemic regions are repeatedly infected with Ct throughout childhood. A proportion of individuals experience prolonged or severe inflammatory episodes that are known to be significant risk factors for ocular scarring in later life. Continued scarring often leads to trichiasis and in-turning of the eyelashes, which causes pain and can eventually cause blindness. The mechanisms driving the chronic immunopathology in the conjunctiva, which largely progresses in the absence of detectable Ct infection in adults, are likely to be multifactorial. Socioeconomic status, education, and behavior have been identified as contributing to the risk of scarring and inflammation. We focus on the contribution of host and pathogen genetic variation, bacterial ecology of the conjunctiva, and host epigenetic imprinting including small RNA regulation by both host and pathogen in the development of ocular pathology. Each of these factors or processes contributes to pathogenic outcomes in other inflammatory diseases and we outline their potential role in trachoma

Expansion of nanoplasmas and laser-driven nuclear fusion in single exploding clusters

The expansion of laser-irradiated clusters or nanodroplets depends strongly on the amount of energy delivered to the electrons and can be controlled by using appropriately shaped laser pulses. In this paper, a self-consistent kinetic model is used to analyze the transition from quasineutral, hydrodinamic-like expansion regimes to the Coulomb explosion (CE) regime when increasing the ratio between the thermal energy of the electrons and the electrostatic energy stored in the cluster. It is shown that a suitable double-pump irradiation scheme can produce hybrid expansion regimes, wherein a slow hydrodynamic expansion is followed by a fast CE, leading to ion overtaking and producing multiple ion flows expanding with different velocities. This can be exploited to obtain intracluster fusion reactions in both homonuclear deuterium clusters and heteronuclear deuterium-tritium clusters, as also proved by three-dimensional molecular-dynamics simulations.Comment: 9 pages, 3 figures, to appear in Plasma Physics and Controlled Fusio

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators

In this paper, we consider one dimensional adiabatic quasi-periodic Schr\"{o}dinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion

Generic Continuous Spectrum for Ergodic Schr"odinger Operators

We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition property. Assuming that the underlying dynamical system satisfies one of these repetition properties, we show using Gordon's Lemma that for a generic continuous sampling function, the associated Schr"odinger operators have no eigenvalues in a topological or metric sense, respectively. We present a number of applications, particularly to shifts and skew-shifts on the torus.Comment: 14 page

The Ten Martini Problem

We prove the conjecture (known as the ``Ten Martini Problem'' after Kac and Simon) that the spectrum of the almost Mathieu operator is a Cantor set for all non-zero values of the coupling and all irrational frequencies.Comment: 31 pages, no figure

X-ray full field microscopy at 30 KeV

In our X-ray full field microscopy experiments, we demonstrated a resolution better than 260 nm over the entire field of view of 80 μm x 80 μm at 30 keV. Our experimental setup at PETRA III, P05, had a length of about 5 m consisting of an illumination optics, an imaging lens and a detector. For imaging, we used a compound refractive lens (CLR) consisting of mr-L negative photo resist, which was fabricated by deep X-ray lithography. As illumination optics, we choose a refractive rolled X-ray prism lens, which was adapted to the numerical aperture of the imaging lens