标题： 依赖范数的外部场随机矩阵系综与超对称性 显示英文标题

标题： Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry

摘要： 研究了在外部场存在下的范数相关随机矩阵系综类。 这些系综中的概率密度依赖于随机矩阵的平方的迹，但除此之外是任意的。 进行了到超空间的精确映射。 推导出一个变换公式，该公式将超空间中的概率密度表示为普通空间中概率密度的单积分。 这是针对正交、酉和辛对称性进行的。 在酉对称性的情况下，得到了关联函数的一些显式结果。 显示英文摘要

摘要： The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact mapping to superspace is performed. A transformation formula is derived which gives the probability density in superspace as a single integral over the probability density in ordinary space. This is done for orthogonal, unitary and symplectic symmetry. In the case of unitary symmetry, some explicit results for the correlation functions are derived.