2024/09/17 by Jingxuan Zhang, Zhang, Jingxuan
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2409.13762
openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove upper bounds on outside probabilities for generic non-autonomous Schrödinger operators on lattices of arbitrary dimension. Our approach is based on a combination of commutator method originated in scattering theory and novel monotonicity estimate for certain mollified asymptotic observables that track the spacetime localization of evolving states. Sub-ballistic upper bounds are obtained, assuming that momentum vanishes sufficiently fast in the front of the wavepackets. A special case gives a refinement of the general ballistic upper bound of Radin-Simon's, showing that the evolution of wavepackets are effectively confined to a strictly linear light cone with explicitly bounded slope. All results apply to long-range Hamiltonian with polynomial decaying off-diagonal terms and can be extended, via a frozen-coefficient argument, to generic nonlinear Schrödinger equations on lattices.