发表机构
Politecnico di Milano; University College, Yonsei University; United Arab Emirates University; Hankyong National University（米兰理工大学; 延世大学校; 阿联酋大学; 韩国汉阳女子大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明齐次开放量子随机游走中均方根弹道速度等于漂移范数，非零漂移导致非常返性，中心化游走在低维常返而高维暂态，并给出势核渐近与可约分解。
AI 中文摘要
我们的研究将均方根弹道输运与有限范围开放量子随机游走的势论常返性联系起来。在具有原始局部通道、有限多个简单的周期傅里叶外围特征值、无非零平稳傅里叶模式以及非退化二次谱项的齐次游走中，我们证明了周期一致局部极限定理，并在非零漂移情况下恢复了指数有限集返回界。中心化情形在至少三维空间中产生强格林函数渐近性，以及在一维和二维空间中的势核渐近性。根据这些假设，均方根弹道速度等于漂移范数，非零漂移表示非常返性，而中心化游走在有效维度一维和二维中是常返的，但在更高维度中是暂态的。低维结果显示了TOM中原点投影的常返性。对于可约游走，显式调和h变换将每个吸收分量转换为OQRW，提供了格林占据势的详细分解。均方根速度的平方是吸收加权的分量漂移平方的平均值，但约化漂移维数分类还需要特定的分量返回估计。一个中心化的非交换族在所有维度上验证了基本谱假设，并提供了显式势常数。精确有限陷阱和稀疏反射屏障为零速度和TOM常返性提供了一种补充的非齐次方法。
英文摘要
Our study connects root-mean-square ballistic transport to potential-theoretic recurrence for finite-range open quantum random walks. In homogeneous walks with primitive local channels, finitely many simple periodic Fourier peripheral eigenvalues, no nonzero stationary Fourier mode, and a nondegenerate quadratic spectral term, we prove a periodic uniform local limit theorem and recover exponential finite-set return bounds for nonzero drift. The centered case yields strong Green-function asymptotics in at least three dimensions, as well as potential-kernel asymptotics in one and two dimensions. According to these assumptions, the RMS ballistic speed equals the drift norm, nonzero drift indicates transience, and centered walks are recurring in effective dimensions one and two but transitory in higher dimensions. The low-dimensional finding shows a recurrence of the origin projection in TOM. For reducible walks, an explicit harmonic \(h\)-transform converts each absorption component to an OQRW, providing a detailed breakdown of Green occupation potentials. The squared RMS speed is the absorption-weighted mean of squared component drifts, but the reduced drift-dimension classification also needs specific component return estimations. A centered noncommuting family validates the fundamental spectral assumptions in all dimensions and provides explicit potential constants. Exact finite traps and sparse reflecting barriers provide a complementary nonhomogeneous method for zero speed and TOM recurrence.
Comments44 pages
