Related papers: Distribution of resonance widths in localized tigh…
This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with…
We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and collectivity that emerges…
We give a detailed analysis of long range cumulative scattering effects from rough boundaries in waveguides. We assume small random fluctuations of the boundaries and obtain a quantitative statistical description of the wave field. The…
Two-dimensional stealthy hyperuniform distributions of rigid scatterers embedded in a waveguide are experimentally characterized the wave transport properties for scalar waves in airborne audible acoustics. The non resonant nature of the…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
Exact method of analytical solution of flat, non-dispersive eigenstates in a class of quasi-one dimensional structures is reported within the tight-binding framework. The states are localized over certain sublattice sites. One such finite…
The frequency dependent time delay correlation function $K(\Omega)$ is studied analytically for a particle reflected from a finite one-dimensional disordered system. In the long sample limit $K(\Omega)$ can be used to extract the resonance…
We address the problem of flat band engineering in different prototypes of quasi-one dimensional kagome network through a generalized analytical proposition worked out within the tight-binding formalism. Exact fabrication of single particle…
The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By…
Scattering theoretical network models for general coherent wave mechanical systems with quenched disorder are investigated. We focus on universality classes for two dimensional systems with no preferred orientation: Systems of spinless…
In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight binding model near two distinct energies in the localized regime. Consequently, with an arbitrary, fixed number n, the asymptotic independence for…
We study the width of a two-body resonance in a coupled-channel system. We demonstrate how the width does not come only determined by the available phase space for its decay to the detection channel, but it greatly depends on the relative…
We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the…
In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
Localized interface states in abrupt semiconductor heterojunctions are studied within a tight-binding model. The intention is to provide a microscopic foundation for the results of similar studies which were based upon the two-band model…
A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…