82 citations · 84 across the 5 of their papers we have counts for
6 papers
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…
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…
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
David Damanik, Mark Embree, Anton Gorodetski +1
We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as ,…
Upper Bounds in Quantum Dynamics
David Damanik, Serguei Tcheremchantsev
We develop a general method to bound the spreading of an entire wavepacket under Schrödinger dynamics from above. This method derives upper bounds on time-averaged moments of the p…
Dynamical Upper Bounds for the Fibonacci Hamiltonian
David Damanik, Serguei Tcheremchantsev
We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for…
Scaling Estimates for Solutions and Dynamical Lower Bounds on Wavepacket Spreading
David Damanik, Serguei Tcheremchantsev
We establish quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators in situations where, in addition to power-law upper bounds on solutions corresponding…