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

The weak localization for the alloy-type Anderson model on a cubic lattice

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e. when the coupling parameter $\lambda$ is small, for the energies $E \le -C \lambda^2$.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy

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

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

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

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

The repulsion between localization centers in the Anderson model

In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together

Localization Bounds for Multiparticle Systems

We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite-range interaction. Two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction. It is established here that for all $n$ there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed through bounds on the transition amplitudes, which are uniform in time and decay exponentially in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the $n$-particle Green function, and related bounds on the eigenfunction correlators

A note on fermions in holographic QCD

We study the fermionic sector of a probe D8-brane in the supergravity background made of D4-branes compactified on a circle with supersymmetry broken explicitly by the boundary conditions. At low energies the dual field theory is effectively four-dimensional and has proved surprisingly successful in recovering qualitative and quantitative properties of QCD. We investigate fluctuations of the fermionic fields on the probe D8-brane and interpret these as mesinos (fermionic superpartners of mesons). We demonstrate that the masses of these modes are comparable to meson masses and show that their interactions with ordinary mesons are not suppressed.Comment: 21+1 pp, 1 figure; v2: typos corrected, refs. adde

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