Spectral theory of quasiperiodic Schrodinger operators
Global theory of quasiperiodic cocycles
Fractal properties of singular continuous measures
Transport theory in quantum physics
Statistical mechanics; Kac equation; and approach to thermodynamic equilibrium
Publications:
Preprints
M. Powell. Large deviation estimates for quasi-periodic Gevrey cocycles. 2025. Preprint available here.
Submitted
F. Bonetto and M. Powell. A Kac system interacting with two heat reservoirs: the shearing case. Preprint available here.
Published/Accepted
(with F. Bonetto and M. Loss). A Kac system interacting with two heat reservoirs. 2026. Comm. Math Physics. To appear. (Available here)
(with W. Liu and X. Wang). Quantum dynamical bounds for long-range operators with skew-shift potentials. 2026. J. Funct. Anal. 290 (2026), no. 9, Paper No. 111378.. (Available here)
(with W. Liu and Y. Tang and X. Wang and R. Zhang and J. Zhou). Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics. 2026. J. Differential Equations to appear.. (Available here)
Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles. 2024. Int. Math. Res. Not. IMRN. 2024 (Available here)
Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background. J. d'Analyse Math. 2024. (Available here)
Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analystic multi-frequency quasiperiodic M(2, C) cocycles. 2024. J. Math Physics (Available here)
(with M. Landrigan). Fine dimensional properties of spectral measures. J. Spectr. Theory. April 2023 (Available here)
(with S. Jitomirskaya). Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrodinger operators with smooth potentials. To appear in Analysis at Large: Dedicated to the Life and Work of Jean Bourgain, Springer ( A. Avila, M. Rassias, Y. G. Sinai, eds.) May 2022. (Available here)
Fractal dimensions of spectral measures of rank one perturbations of a positive self-adjoint operator. J. Math. Anal. App., 475(2):1803–1817, July 2019. (Available here)