122 citations · 452 across the 56 of their papers we have counts for
39 papers · 1 filter
Spectral Analysis of Lattice Schrödinger-Type Operators Associated with the Nonstationary Anderson Model and Intermittency
Dan Han, Stanislav Molchanov, Boris Vainberg
The research explores a high irregularity, commonly referred to as intermittency, of the solution to the non-stationary parabolic Anderson problem: \begin{equation*} \frac{\partial…
Propagation and dispersion of Bloch waves in periodic media with soft inclusions
Yuri A. Godin, Boris Vainberg
We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisf…
Absolutely continuous and pure point spectra of discrete operators with sparse potentials
S. Molchanov, O. Safronov, B. Vainberg
We consider the discrete Schrödinger operator with a sparse potential and find conditions guaranteeing either existence of wave operators for the pair and …
On the Near-Critical Behavior of Continuous Polymers
L. Koralov, S. Molchanov, B. Vainberg
The aim of this paper is to investigate the distribution of a continuous polymer in the presence of an attractive finitely supported potential. The most intricate behavior can be o…
The Radius of a Polymer at a Near-Critical Temperature
L. Koralov, S. Molchanov, B. Vainberg
We consider a mean-field model of a polymer with a spherically-symmetric finitely supported potential. We describe how the typical size of the polymer depends on the two parameters…
Dispersive and effective properties of two-dimensional periodic media
Yuri A. Godin, Boris Vainberg
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation…