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4 papers
Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles
Matthew Powell
It is known that the Lyapunov exponent of analytic 1-frequency quasiperiodic cocycles is continuous in cocycle and, when the frequency is irrational, jointly in cocycle and frequen…
Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background
Matthew Powell
We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schrödinger operators with an added finite valued background potential. We prove that, fo…
Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials
Svetlana Jitomirskaya, Matthew Powell
We present a method for obtaining power-logarithmic bounds on the growth of the moments of the position operator for one-dimensional ergodic Schrödinger operators. We use Bourgain'…
Fine dimensional properties of spectral measures
Michael Landrigan, Matthew Powell
Operators with zero dimensional spectral measures appear naturally in the theory of ergodic Schrödinger operators. We develop the concept of a complete family of Hausdorff measure…