The spectral theory of linear operators plays a key role in the mathematical formulation of
quantum theory. This textbook provides a concise and comprehensible introduction to the …

The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from
dynamical systems, topology, and analysis. Additionally, this setting includes many models …

We investigate the Anderson metal-insulator transition for random Schrödinger operators.
We define the strong insulator region to be the part of the spectrum where the random …

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 λ → ∞,\rm dim …

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 …

We investigate the equivalence between dynamical localization and localization properties
of eigenfunctions of Schrödinger Hamiltonians. We introduce three classes of equivalent …

We introduce a notion of ˇ-almost periodicity and prove quantitative lower spectral/quantum
dynamical bounds for general bounded ˇ-almost periodic potentials. Applications include the …

We consider ergodic families of Schrödinger operators over base dynamics given by strictly
ergodic subshifts on finite alphabets. It is expected that the majority of these operators have …

We construct examples of potentials $ V (x) $ satisfying $| V (x)|\leq\frac {h (x)}{1+ x}, $ where
the function $ h (x) $ is growing arbitrarily slowly, such that the corresponding Schrödinger …

Power law logarithmic bounds of moments for long range operators in arbitrary dimension |
Journal of Mathematical Physics | AIP Publishing Skip to Main Content Umbrella Alt Text …