62 citations · 366 across the 29 of their papers we have counts for
32 papers
Smooth perturbation theory and generic Cantor spectrum for multi-dimensional monotone quasiperiodic operators
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We consider multi-dimensional quasiperiodic Schrödinger operators with monotone sawtooth-type potentials in the perturbative localization regime. We prove that a given gap is close…
Perturbative diagonalization and spectral gaps of quasiperiodic operators on with monotone potentials
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We obtain a perturbative proof of localization for quasiperiodic operators on with one-dimensional phase space and monotone sampling functions, in the regime of smal…
On gaps in the spectra of quasiperiodic Schrödinger operators with discontinuous monotone potentials
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We show that, for one-dimensional discrete Schrödinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectra…
Classical Wave methods and modern gauge transforms: Spectral Asymptotics in the one dimensional case
Jeffrey Galkowski, Leonid Parnovski, Roman Shterenberg
In this article, we consider the asymptotic behaviour of the spectral function of Schrödinger operators on the real line. Let have the form…
The almost periodic gauge transform -- An abstract scheme with applications to Dirac Operators
Jean Lagacé, Sergey Morozov, Leonid Parnovski +2
One of the main tools used to understand both qualitative and quantitative spectral behaviour of periodic and almost periodic Schrödinger operators is the method of gauge transform…
Ballistic Transport for Schrödinger Operators with Quasi-periodic Potentials
Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg
We prove the existence of ballistic transport for a Schrödinger operator with a generic quasi-periodic potential in any dimension .