We investigate spreading rates of one-dimensional quantum states under the Schrödinger time-evolution. The focus of this paper is on the states that either have finite support or decay exponentially at [Formula: see text]. In particular, we extend results of Damanik and Tcheremchantsev on estimating transport exponents that were originally proved to hold for the initial states supported on a single site. These general upper and lower estimates are then applied to several classes of models, including Sturmian, quasi-periodic and substitution-generated potentials, and the random polymer model.

中文翻译：

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有大量支持的州的运输指数

我们研究了薛定谔时间演化下一维量子态的扩散率。本文的重点是在[公式：见文本]处具有有限支持或呈指数衰减的状态。特别是，我们扩展了 Damanik 和 Tcheremchantsev 关于估计最初证明在单个站点上支持的初始状态的传输指数的结果。然后将这些一般的上限和下限估计应用于几类模型，包括 Sturmian、准周期和替代产生的势以及随机聚合物模型。