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arXiv · 2608.29339

Sharp Logarithmic Quantum Dynamics for Quasiperiodic Schr\"odinger Operators

Wencai Liu·Xueyin Wang
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Abstract

Dynamical localization requires all position moments of a quantum wavepacket to remain bounded in time, but for quasiperiodic Schr\"odinger operators such bounds are generally not uniform in phase. In the positive Lyapunov exponent regime, the best known phase-uniform estimates instead grow on a logarithmic scale. We prove that both the logarithmic scale and the dependence on the moment order are sharp for a class of one-frequency quasiperiodic Schr\"odinger operators with even potentials. Our main ingredient is a reflective version of semi-uniformly localized eigenfunctions, adapted to the two localization centers forced by a completely resonant phase, from which we obtain matching logarithmic lower bounds along sequences of times.

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Wencai Liu, Xueyin Wang. 2026-08-29. Sharp Logarithmic Quantum Dynamics for Quasiperiodic Schr\"odinger Operators. https://arxiv.org/abs/2608.29339

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