Related papers: A continuum limit for the Kronig-Penney model
A derivative nonlinear Schrodinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant eta. The ranges of eta within each band can be completely determined using number…
I explore a theory of transport and optical properties of strange metallic carriers in strongly correlated systems that follows from assuming that the diffusion constant has reached its quantum limit $D=\hbar/m$, and that such quantum…
We consider a quantum particle in a periodic structure submitted to a constant external electromotive force. The periodic background is given by a smooth potential plus singular point interactions and has the property that the gaps between…
A parabolic-parabolic (Patlak-) Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy…
We investigate the propagation of waves in one-dimensional systems with L\'evy-type disorder. We perform a complete analysis of non-relativistic and relativistic wave transmission submitted to potential barriers whose width, separation or…
In this paper, we use the 'Quasi Normal Modes' (QNM) approach for discussing the transmission properties of double-side opened optical cavities: in particular, this approach is specified for one dimensional (1D) 'Photonic Band Gap' (PBG)…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
We consider a periodic quantum graph in the form of a rectangular lattice with the $\delta$-coupling of strength $\gamma$ in the vertices perturbed by changing the latter at an infinite straight array of vertices to a…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically-nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear…
We investigate topological phenomena in a spatially modulated Dirac-$\delta$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy…
We studied electromagnetic wave propagation in a system that is periodic in both space and time, namely a discrete 2D transmission line (TL) with capacitors modulated in tandem externally. Kirchhoff's laws lead to an eigenvalue equation…
The CP(N-1) \sigma\ model on finite interval of length R with Dirichlet boundary conditions is analysed in the 1/N expansion. The theory has two phases, separated by a phase transition at R ~ 1/\Lambda, \Lambda\ is dynamical scale of the…
We study the equilibrium properties of a quantum dot connected to a bulk lead by a single-mode quantum point contact. The ground state energy and other thermodynamic characteristics of the grain show periodic dependence on the gate voltage…
In this paper, the interaction and transmission time of quantum density solitons waves representing particles passing through finite barrier potentials is investigated. Using the conservation of energy and of quantum density, it is first…
Motivated by the $\Sigma$-hypernuclear states reported in ($K^-,\pi^{\pm}$) experiments, we have explored the possibility that there exists a particle-stable $\Sigma^- nn$ bound state. For the J\"ulich \~A hyperon-nucleon, realistic-force…
We study the tunneling of slow quantum packets through a high Coulomb barrier. We show that the transmission coefficient can be quite different from the standard expression obtained in the plane wave (WKB) approximation (and larger by many…
We derive an effective one-dimensional limit from a three-dimensional Kelvin-Voigt model for viscoelastic thin-walled beams, in which the elastic and the viscous stress tensor comply with a frame-indifference principle. The limiting system…