随机XNOR跳跃模型中的异常电流涨落
Anomalous current fluctuations in the stochastic XNOR hopping model
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中文总结 AI 辅助
针对随机XNOR跳跃模型，研究其自旋电流涨落，提出三个带明确振幅的长时间电流分布猜想，通过模拟提供数值支持，相关证明由AI生成。
中文摘要 AI 辅助
我们研究一维动力学约束跳跃模型——随机XNOR过程中自旋电流的涨落。针对长时间电流分布，我们提出三个带明确振幅的猜想：非零磁化的均匀初始态在t^(1/4)尺度上呈高斯极限；具有相反磁化的畴壁态在t^(1/4)尺度上呈半正态极限；零磁化的均匀初始态在t^(1/8)尺度上呈M-Wright极限。早期工作已识别示踪机制，并预判了畴壁和零磁化场景的标度指数与极限形状。我们从微观XNOR动力学出发，预测了连续时间过程缺失的振幅，并将该图像扩展至均匀偏置初始数据。模拟为所有三个猜想提供了无拟合参数的数值支持，一篇独立的数学 companion paper 给出了经AI生成的候选证明，本研究及写作流程中使用了生成式AI工具。
英文摘要
We consider fluctuations of the spin current in the stochastic XNOR process, a kinetically constrained hopping model in one spatial dimension. We formulate three conjectures with explicit amplitudes for the long-time current distributions: a Gaussian limit on the $t^{1/4}$ scale for homogeneous initial states with nonzero magnetization, a half-normal limit on the $t^{1/4}$ scale for domain-wall states with opposite magnetizations, and an M-Wright limit on the $t^{1/8}$ scale for homogeneous initial states at zero magnetization. Earlier work identified the tracer mechanism and anticipated the scaling exponents and limiting shapes in the domain-wall and zero-magnetization settings. Starting from the microscopic XNOR dynamics, we predict the missing amplitudes for the continuous-time process and extend the picture to homogeneous biased initial data. Simulations provide numerical support for all three conjectures without fitted parameters. A separate mathematical companion paper presents an extensively AI-generated candidate proof. Generative-AI tools were used in the research and writing workflow.
发表机构
- MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group（MTA-ELTE “Momentum”可积量子动力学研究组）
- ELTE Eötvös Loránd University（布达佩斯罗兰大学）
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