23 citations · 65 across the 19 of their papers we have counts for
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On the structure of band edges of 2d periodic elliptic operators
Nikolay Filonov, Ilya Kachkovskiy
For a wide class of 2D periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated.
All couplings localization for quasiperiodic operators with Lipschitz monotone potentials
Svetlana Jitomirskaya, Ilya Kachkovskiy
We establish Anderson localization for quasiperiodic operator families of the form for all and all Diophantine , provided that…
On transport properties of isotropic quasiperiodic spin chains
Ilya Kachkovskiy
We consider isotropic spin chains whose magnetic potentials are quasiperiodic and the effective one-particle Hamiltonians have absolutely continuous spectra. For a wide class…
-reducibility and localization for quasiperiodic operators
Svetlana Jitomirskaya, Ilya Kachkovskiy
We give a simple argument that if a quasiperiodic multi-frequency Schrödinger cocycle is reducible to a constant rotation for almost all energies with respect to the density of sta…