Physics – Mathematical Physics
Scientific paper
2004-02-25
Physics
Mathematical Physics
5 pages
Scientific paper
We prove absence of absolutely continuous spectrum for discrete one-dimensional Schr\"odinger operators on the whole line with certain ergodic potentials, $V_\omega(n) = f(T^n(\omega))$, where $T$ is an ergodic transformation acting on a space $\Omega$ and $f: \Omega \to \R$. The key hypothesis, however, is that $f$ is discontinuous. In particular, we are able to settle a conjecture of Aubry and Jitomirskaya--Mandel'shtam regarding potentials generated by irrational rotations on the torus. The proof relies on a theorem of Kotani, which shows that non-deterministic potentials give rise to operators that have no absolutely continuous spectrum.
Damanik David
Killip Rowan
No associations
LandOfFree
Ergodic Potentials With a Discontinuous Sampling Function Are Non-Deterministic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ergodic Potentials With a Discontinuous Sampling Function Are Non-Deterministic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ergodic Potentials With a Discontinuous Sampling Function Are Non-Deterministic will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-485003