82 citations · 84 across the 5 of their papers we have counts for
Showing math-phShow all
3 papers · 1 filter
math-ph2007★ 82 cited
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 ,…
math-ph2005★ 1 cited
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…
math-ph2004★ 1 cited
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…