5 papers · 1 filter
Capacity and measure approximations for Schrödinger operators
Burak HatinoÄlu, Svetlana Jitomirskaya
We prove that logarithmic capacity convergence for phase-union spectra of quasi-periodic Schrödinger operators in the zero Lyapunov exponent regime is robust, requiring only conti…
Intrinsic Symplectic Structure and Sharp Arithmetic Universality
Lingrui Ge, Svetlana Jitomirskaya
We show that formal eigenvalue equations of analytic one-frequency Schröd-inger operators admit intrinsic analytic $Sp(2k,\C)$ structures, where is the T-acceleration in…
Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition
Svetlana Jitomirskaya, Wencai Liu, Serguei Tcheremchantsev
We develop tools to study arithmetically induced singular continuous spectrum in the neighborhood of the arithmetic transition in the hyperbolic regime. This leads to first transit…
Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation
Svetlana Jitomirskaya, Ilya Kachkovskiy
We obtain the sharp arithmetic Gordon's theorem: that is, absence of eigenvalues on the set of energies with Lyapunov exponent bounded by the exponential rate of approximation of f…
Sharp arithmetic localization for quasiperiodic operators with monotone potentials
Svetlana Jitomirskaya, Ilya Kachkovskiy
We prove the universality of sharp arithmetic localization for all one-dimensional quasiperiodic Schrödinger operators with anti-Lipschitz monotone potentials.