Role of dimensionality in the Anderson transition at strong disorder

Determine how spatial dimensionality influences the Anderson transition in the strong-disorder regime of Anderson localization, specifically characterizing the dependence of transition behavior and fluctuation properties on dimension and clarifying the organizing principles governing this regime.

Background

This paper establishes extensive numerical evidence that fluctuations in two-dimensional Anderson localization fall within the (1+1)-dimensional Kardar–Parisi–Zhang (KPZ) universality class, both for localized eigenstates and for long-time evolved wave packets. It further reveals glassy features analogous to directed polymer physics, such as dominant paths exhibiting pinning and avalanche behavior.

While the study provides a unified KPZ framework for 2D, the authors highlight that the situation in higher dimensions is richer and less understood. They point to the inherently more complex (d+1)-dimensional directed polymer problem and identify the need to clarify how dimensionality affects the Anderson transition under strong disorder, indicating this as an important open question currently under active debate.