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4 papers · 2 filters
Localization on quantum graphs with random edge lengths
Frédéric Klopp, Konstantin Pankrashkin
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lat…
One-dimensional space-discrete transport subject to Levy perturbations
I. Pavlyukevich, I. M. Sokolov
In this paper we study a one-dimensional space-discrete transport equation subject to additive Levy forcing. The explicit form of the solutions allows their analytic study. In part…
Lagrangian and Hamiltonian two-scale reduction
Johannes Giannoulis, Michael Herrmann, Alexander Mielke
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dy…
Semiclassical reduction for magnetic Schroedinger operator with periodic zero-range potentials and applications
Bernard Helffer, Konstantin Pankrashkin
The two-dimensional Schroedinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields we reduce the spectral problem t…