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

Lifshitz tails for alloy type models in a constant magnetic field

In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type $e^{-\log^2|E-2bq|}$

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

On the Mott formula for the a.c. conductivity and binarycorrelators in the strong localization regime of disordered systems.

27 pages, 2 figures, LateX, submitted to J.Phys.A.We present a method that allows us to find asymptotic form of various characteristics of disordered systems in the strong localization regime, i.e., when either the random potential is big enough or the energy is close enough to the spectrum edges. The method is based on the hypothesis that relevant realizations of the random potential in the strong localization regime have the form of deep random wells that are uniformly and chaotically distributed in the space with a sufficiently small density. Assuming this and using the density expansion, we show first that the density of wells coincides in the leading order with the density of states. Thus the density of states is in fact the small parameter of the theory in the strong localization regime. Then we derive the Mott formula for the low frequencyconductivity and the asymptotic formulas for certain two-point correlators when the difference of respective energies is small

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Cardiac arrest and COVID-19: inflammation, angiotensin-converting enzyme 2, and the destabilization of non-significant coronary artery disease-a case report.

The new β-coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) appears to exhibit cardiovascular pathogenicity through use of angiotensin-converting enzyme 2 (ACE2) for cell entry and the development of a major systemic inflammation. Furthermore, cardiovascular comorbidities increase susceptibility to SARS-CoV-2 infection and the development of a severe form of COronaVIrus Disease 2019 (COVID-19). We describe the case of a COVID-19 patient whose inaugural presentation was a refractory cardiac arrest secondary to the destabilization of known, non-significant coronary artery disease. Patient was supported by venoarterial extracorporeal life support. After 12 h of support, cardiac function remained stable on low vasopressor support but the patient remained in a coma and brainstem death was diagnosed. Myocardial injury is frequently seen among critically unwell COVID-19 patients and increases the risk of mortality. This case illustrates several potential mechanisms that are thought to drive the cardiac complications seen in COVID-19. We present the potential role of inflammation and ACE2 in the pathophysiology of COVID-19

Preheating after N-flation

We study preheating in N-flation, assuming the Mar\v{c}enko-Pastur mass distribution, equal energy initial conditions at the beginning of inflation and equal axion-matter couplings, where matter is taken to be a single, massless bosonic field. By numerical analysis we find that preheating via parametric resonance is suppressed, indicating that the old theory of perturbative preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity parameters and the scalar spectral index computed for N-flation are similar to those in single field inflation (at least within an observationally viable parameter region), our results suggest that the physics of preheating can differ significantly from the single field case.Comment: 14 pages, 14 figures, references added, fixed typo