Quasiperiodic systems extend the concept of Anderson transition to quasirandom and low-dimensional realms and have garnered widespread attention. Here, we propose asymptotic quasiperiodic two-dimensional systems characterized by a sequence of rational magnetic fluxes, which have an irrational limit, and predict exotic universal wave-packet dynamics and transport phenomena associated with asymptotic quasiperiodicity (AQP). The predictions unveil a class of multiple metal-insulator transitions driven by the interplay between AQP, relaxation, and finite temperature, which further reveals a unified and profound mechanism. Specifically, all the transport phenomena, including the wave-packet dynamics, the bulk and edge transport, are unified in the universal scaling laws unveiled in the asymptotic quasiperiodic regime, which demonstrate a nontrivial asymptotic connection to quantum phases in the quasiperiodic limit. Our work enriches the universal quantum transport phenomena, adding to the basic mechanisms underlying metal-insulator transitions, and opens up an avenue to study the exotic transport physics with AQP in high dimensions.

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• Anderson localization
• Edge states
• Electrical conductivity
• Metal-insulator transition
• Quantum Hall effect
• Topological phases of matter
• Transport phenomena