Recursion scheme for the largest β-Wishart–Laguerre eigenvalue and Landauer conductance in quantum transport
Recursion scheme for the largest β-Wishart–Laguerre eigenvalue and Landauer conductance in quantum transport
复制标题
量子输运中最大 β-Wishart-Laguerre 特征值和 Landauer 电导的递归方案
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Santosh Kumar
中科院分区：
文献类型：
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作者：
P. Forrester;Santosh Kumar
以Dyson参数和Laguerre参数a为指标的Wishart-Laguerre集合的最大特征值分布是多元统计的基础，在各个领域都有应用。基于Selberg积分的推广，我们提供了一种有效的递推方案来显式地计算非负整数和有限矩阵大小的原始模型和固定轨迹变量的分布。因为这规避了已知的基于行列式的符号计算，这些行列式对于大尺寸来说是不切实际的。我们的精确结果在多通道通信和双部纠缠领域有直接的应用。此外，我们还精确地解决了一个长期存在的问题，即在具有两个理想引线的混沌介观腔中寻找兰道尔电导分布的一般结果。到目前为止，精确的封闭形式的结果只能在傅里叶-拉普拉斯空间中得到，或者只能在逐个案例的基础上得到。
The largest eigenvalue distribution of the Wishart–Laguerre ensemble, indexed by Dyson parameter and Laguerre parameter a, is fundamental in multivariate statistics and finds applications in diverse areas. Based on a generalisation of the Selberg integral, we provide an effective recursion scheme to compute this distribution explicitly in both the original model, and a fixed-trace variant, for non-negative integers and finite matrix size. For this circumvents known symbolic evaluation based on determinants which become impractical for large dimensions. Our exact results have immediate applications in the areas of multiple channel communication and bipartite entanglement. Moreover, we are also led to the exact solution of a long standing problem of finding a general result for Landauer conductance distribution in a chaotic mesoscopic cavity with two ideal leads. Thus far, exact closed-form results for this were available only in the Fourier–Laplace space or could be obtained on a case-by-case basis.
影响因子：
5.4
作者：
Kortun, Ayse;Sellathurai, Mathini;Zhong, Caijun
通讯作者：
Zhong, Caijun