奇异量子踢转子的长程非线性西格玛模型
Long-range Nonlinear Sigma Model for a Singular Quantum Kicked Rotor
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中文总结 AI 辅助
该研究针对奇异量子踢转子与幂律随机带矩阵（PRBM）的关联问题，推导非局域超对称非线性西格玛模型，经两圈阶重整化群分析，发现匹配对称性类别和耦合约定后，转子可重现PRBM的长程安德森转变。
中文摘要 AI 辅助
长期以来，奇异踢转子因动量空间Floquet矩阵元素呈代数衰减，被与幂律随机带矩阵（PRBM）进行比较。但目前仍不清楚，转子的确定性关联在长距离下是否变得无关紧要，以及在何种条件下这两个系统共享相同的红外理论。为解决该问题，我们直接从具有幂律或对数奇异性的量子踢转子推导非局域超对称非线性西格玛模型。通过进行两圈阶的重整化群分析，我们表明，在匹配对称性类别和耦合约定后，转子重现了对应PRBM的长程安德森转变，包括其局域、临界和扩展红外 regime。
英文摘要
Singular kicked rotors have long been compared with power-law random banded matrices (PRBM) because their momentum-space Floquet matrix elements decay algebraically. However, it has remained unclear whether the deterministic correlations of the rotor become irrelevant at long distances and, consequently, under what conditions the two systems share the same infrared theory. To address this question, we derive a nonlocal supersymmetric nonlinear sigma model directly from a quantum kicked rotor with a power-law or logarithmic singularity. By carrying out the renormalization-group analysis up to two-loop order, we show that, after matching the symmetry class and coupling convention, the rotor reproduces the long-range Anderson transition of the corresponding PRBM, including its localized, critical, and extended infrared regimes.
