122 citations · 139 across the 15 of their papers we have counts for
11 papers · 1 filter
On the Emergence of Discrete Spectrum for Weakly Disordered Schrödinger Operators
Stanislav Molchanov, Oleg Safronov
We investigate the spectral properties of the Anderson operator perturbed by a localized negative potential, \(-V\). Specifically, we analyze the random Schrödinger operator define…
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…
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…
On mathematical foundation of the Brownian motor theory
L. Koralov, S. Molchanov, B. Vainberg
The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes…
On the negative spectrum of the hierarchical Schrödinger operator
S. Molchanov, B. Vainberg
This paper is devoted to the spectral theory of the Schrödinger operator on the simplest fractal: Dyson's hierarchical lattice. An explicit description of the spectrum, eigenfuncti…
Non-Random Perturbations of the Anderson Hamiltonian in the 1-D case
J. Holt, S. Molchanov, B. Vainberg
Recently (see Molchanov & Vainberg 2011), two of the authors applied the Lieb method to the study of the negative spectrum for particular operators of the form . Here, $H_…
Wave propagation in periodic networks of thin fibers
S. Molchanov, B. Vainberg
We will discuss a one-dimensional approximation for the problem of wave propagation in networks of thin fibers. The main objective here is to describe the boundary (gluing) conditi…
Propagation of Waves in Networks of Thin Fibers
S. Molchanov, B. Vainberg
The paper contains a simplified and improved version of the results obtained by the authors earlier. Wave propagation is discussed in a network of branched thin wave guides when th…
On general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities
S. Molchanov, B. Vainberg
These classical inequalities allow one to estimate the number of negative eigenvalues and the sums for a wide class of Schrödinger operators. We provide a detail…
Laplace Operator in Networks of Thin Fibers: Spectrum Near the Threshold
S. Molchanov, B. Vainberg
Our talk at Lisbon SAMP conference was based mainly on our recent results (published in Comm. Math. Phys.) on small diameter asymptotics for solutions of the Helmgoltz equation in…
Scattering solutions in a network of thin fibers: small diameter asymptotics
S. Molchanov, B. Vainberg
Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting…