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math.SP2025
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…
math.SP2008
Quantum Dynamics via Complex Analysis Methods: General Upper Bounds Without Time-Averaging and Tight Lower Bounds for the Strongly Coupled Fibonacci Hamiltonian
David Damanik, Serguei Tcheremchantsev
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we deriv…