相关论文: Density of reflection resonances in one-dimensiona…
We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is…
We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at…
We calculate the correlator of the local density of states <\rho_{E}(r_1)\rho_{E+\omega}(r_2)> in quasi-one-dimensional disordered wires in a magnetic field, assuming that |r_1-r_2| is much smaller than the localization length. This amounts…
We introduce a unified approach that, given a strong gravitationally lensed polarised source, self-consistently infers its complex surface brightness distribution and the lens galaxy mass-density profile, magnetic field and electron density…
This work further develops the calculation of QED effects in a finite Gaussian basis. We focus on the non-linear ${\alpha}(Z{\alpha})^{n\ge 3}$ contribution to the vacuum polarization density, computing the energy shift of 1s$_{1/2}$ states…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of…
A simple 1-D relativistic model for a diatomic molecule with a double point interaction potential is solved exactly in a constant electric field. The Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density function, allowing…
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…
Resonances in the reflection probability amplitude r(E) can occur in energy ranges in which the reflection probability R(E)=|r(E)|^2 is 1. They occur as the phase phi(E) defined by r(E) = t*(E)/t(E) = 1e^{i 2phi(E)} undergoes a rapid change…
We develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
The reflectionless transmission resonances in above-barrier reflection of Bose-Einstein condensates by the Rosen-Morse potential are considered using the mean field Gross-Pitaevskii approach. Applying an exact third order nonlinear…
The mean and the variance of the logarithm of the conductance ($ln g$) in the localized regime in the one-dimensional Anderson model are calculated analytically for weak disorder, starting from the recursion relations for the complex…
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…
We consider multi-dimensional Schr\"odinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on…