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:
F. Bonetto and M. Loss and M. Powell. The two-reservoir 3D Kac evolution. 2024. In Preparation
W. Liu and M. Powell and X. Wang. Quantum dynamical bounds for long-range operators with skew-shift potentials. 2024. In Preparation
M. Powell. Continuity of the Lyapunov exponent for Gevrey multi-frequency quasiperiodic cocycles. 2024. In Preparation
M. Powell. Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles. To appear IMRN 2024. arXiv:2210.09285 (Available here)
M. Powell. Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background. J. d'Analyse Math, to appear. 2024. (Available here)
M. Powell. Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analystic multi-frequency quasiperiodic M(2, C) cocycles. 2023. JMP (Available here)
M. Landrigan and M. Powell. Fine dimensional properties of spectral measures. J. Spectr. Theory. April 2023 (Available here)
S. Jitomirskaya and M. Powell. 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)
M. Powell. 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)