具有重尾跳变幅度的安德森模型中反常扩散的分析理论
Analytical Theory for Anomalous Diffusion in the Anderson Model with Heavy Tails
AI总结：
该研究针对具有重尾跳变幅度的非相互作用安德森模型建立反常输运分析理论，推导均方位移时间依赖关系，发现稀有跳变过程可作为单粒子机制产生反常输运，为区分两类动力学提供基准。
AI中文摘要：
我们针对具有重尾跳变幅度的非相互作用安德森模型，建立了反常输运的分析理论。尽管不存在相互作用或真正的多体效应，跳变幅度的宽分布仍会产生具有亚扩散有效指数的扩展中间时间区域。通过解析求解输运方程，我们推导了均方位移的时间依赖关系，并确定了从中间反常区域到渐近扩散输运的连续交叉。当趋近局域化相变时，亚扩散窗口的空间范围会参数式发散，而以Γ₀⁻¹为单位向常规扩散的交叉仍保持有限。这会在空间中产生越来越宽的反常输运区域，与多体局域化相变附近观测到的格里菲斯型输运极为相似。我们的结果表明，仅稀有跳变过程就为稳健的输运反常提供了微观单粒子机制，为区分相互作用诱导效应与无序驱动动力学建立了分析基准。
英文摘要：
We develop an analytical theory of anomalous transport in a noninteracting Anderson model with heavy-tailed hopping amplitudes. The broad distribution of hopping amplitudes gives rise to an extended intermediate-time regime with a subdiffusive effective exponent, despite the absence of interactions or genuine many-body effects. By solving the transport equations analytically, we derive the time dependence of the mean-square displacement and identify a continuous crossover from an intermediate anomalous regime to asymptotically diffusive transport. As the localization transition is approached, the spatial extent of the subdiffusive window diverges parametrically, while the crossover to conventional diffusion remains finite in units of $Γ_0^{-1}$. This produces an increasingly broad anomalous transport regime in space that can closely resemble Griffiths-type transport observed near the many-body localization transition. Our results demonstrate that rare hopping processes alone provide a microscopic single-particle mechanism for robust transport anomalies, establishing an analytical benchmark for distinguishing interaction-induced effects from disorder-driven dynamics.
