Related papers: Wave localization in number-theoretic landscapes
In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…
In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields. In particular, we address…
Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can…
The spectral landscape and the transport property of a translationally invariant network with side-coupled quantum dots are demonstrated within the tight-binding framework. For periodic environment band structure is demonstrated…
In this paper, we investigate the localization properties of optical waves in disordered systems with multifractal scattering potentials. In particular, we apply the localization landscape theory to the classical Helmholtz operator and,…
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…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. This dispersion is associated with the continuous spectrum of…
Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large scales characterized by few variables such as the particle number density, temperature and pressure obeying a set of hydrodynamic (or macroscopic) equations. Does…
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…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…
We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest…
The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schroedinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator.…
We apply variational-wavelet approach for constructing multiscale high-localized eigenmodes expansions in different models of nonlinear waves. We demonstrate appearance of coherent localized structures and stable pattern formation in…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We study the localization of wave functions for one-dimensional Schr\"odinger Hamiltonians with random potentials $V(x)$ with short range correlations and large local fluctuations such that $\int\D{x} \smean{V(x)V(0)}=\infty$. A random…
We study acoustic propagation in one dimensional water ducts containing many air-filled blocks. The acoustic band structures for the periodic arrangements of the blocks is calculated, whereas the transmission for various random…
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…