时间反演不变性破缺对散射矩阵非对角元及截面分布的影响
Influence of Time Reversal Invariance Breaking on the Distribution of Off-Diagonal Scattering Matrix Elements and Cross Sections
- Fakultät für Physik, Universität Duisburg–Essen（杜伊斯堡-埃森大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文利用超对称方法推导了时间反演不变性破缺系统中散射矩阵非对角元及截面的精确分布，发现分布对称而矩阵元不对称，有助于数据分析。
AI中文摘要：
散射理论是研究量子系统的关键工具。普适方法尤其受到关注，特别是在随机矩阵理论的框架下。戴森的三重分类法根据系统在时间反演下的行为对其进行分类。在这三种情形下，散射矩阵非对角元及截面的分布最近已被计算出来。然而，在许多应用中，系统既非完全保持也非完全破缺时间反演不变性，例如处于可调外磁场中的系统。对这些系统的研究历史悠久，在随机矩阵理论中亦如此。我们研究了时间反演不变性破缺对上述分布普适行为的影响。利用超对称方法，我们成功推导出了在无其他对称性且具有半整数或整数/无自旋的系统中，散射矩阵非对角元及截面分布的精确表达式。我们发现这些分布是对称的，而散射矩阵元则不对称。此外，我们的结果可能大大便利时间反演不变性破缺的数据分析。
英文摘要：
Scattering theory is a key tool for the investigation of quantum systems. Universal approaches are of interest, particularly in the framework of Random Matrix Theory. Dyson's Threefold way classifies systems according to their behavior under time reversal. In these three cases the distribution of off-diagonal scattering matrix elements and cross sections were recently calculated. However, in many applications systems neither display full nor fully broken time reversal invariance, such as systems in tuneable external magnetic fields. The study of these systems has a long history, also in Random Matrix Theory. We investigate the influence of time reversal invariance breaking on the universal behavior of the mentioned distributions. Using supersymmetry we succeed in deriving exact expressions for the distribution of off-diagonal scattering matrix elements and cross sections in systems with half-integer or integer/no spin in the absence of further symmetries. We find that the distributions are symmetric while the scattering matrix elements are not. Furthermore, our results might considerably facilitate the data analysis of time reversal invariance breaking.
