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math-ph2026
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…
math-ph2024
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…
math-ph2020
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…