Spectral flow and level spacing of edge states for quantum Hall hamiltonians

We consider a non relativistic particle on the surface of a semi-infinite cylinder of circumference $L$ submitted to a perpendicular magnetic field of strength $B$ and to the potential of impurities of maximal amplitude $w$. This model is of importance in the context of the integer quantum Hall effect. In the regime of strong magnetic field or weak disorder $B>>w$ it is known that there are chiral edge states, which are localised within a few magnetic lengths close to, and extended along the boundary of the cylinder, and whose energy levels lie in the gaps of the bulk system. These energy levels have a spectral flow, uniform in $L$, as a function of a magnetic flux which threads the cylinder along its axis. Through a detailed study of this spectral flow we prove that the spacing between two consecutive levels of edge states is bounded below by $2\pi\alpha L^{-1}$ with $\alpha>0$, independent of $L$, and of the configuration of impurities. This implies that the level repulsion of the chiral edge states is much stronger than that of extended states in the usual Anderson model and their statistics cannot obey one of the Gaussian ensembles. Our analysis uses the notion of relative index between two projections and indicates that the level repulsion is connected to topological aspects of quantum Hall systems.Comment: 22 pages, no figure

Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

TRα Mutations in Human

Resistance to thyroid hormone alpha is an emerging syndrome, with up to now a limited number of published cases. Some features are common to most of the patients, but there is still some work to provide a comprehensive description of the full spectrum of the syndrome. A survey of the strategy to screen for and characterize the mutations in TR α gene is given

Expert opinion on pituitary complications in immunotherapy

Hypophysitis is a frequent toxic endocrine side-effect of immunotherapy. Prevalence is higher with anti-CTLA-4 antibodies (4-20%) or in association with PD-1 inhibitors (8%). Diagnosis is presumptive, based on poorly specific clinical symptoms (usually, headache and asthenia) and/or hyponatremia and/or at least one pituitary deficit and/or abnormal imaging. Visual disorder or polyuropolydipsic syndrome are exceptional. In decreasing order of frequency, deficits are thyrotropic (86-100%), gonadotropic (85-100%) or corticotropic (50-73%); somatotropin deficit or abnormal prolactin level are rarer. Pituitary MRI in acute phase shows variable moderate increase in pituitary volume, ruling out differential diagnoses, especially pituitary metastasis. Treatment of corticotropin deficiency requires systematic emergency replacement therapy, with the usual modalities, while treatment of other deficits depends on clinical status and progression. Thyrotropin and gonadotropin deficits usually recover, but corticotropin deficiency persists over the long term, requiring education and specialized endocrinologic follow-up. Onset of hypophysitis does not contraindicate continuation of immunotherapy and does not usually require high dose synthetic glucocorticoids

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schroedinger operators

We show for a large class of discrete Harper-like and continuous magnetic Schrodinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by J. Bellissard in 1994, and give examples in favor of a recent conjecture of G. Nenciu.Comment: 15 pages, accepted for publication in Annales Henri Poincar