无序玻色子随机矩阵模型的一种构造方法
A method for constructing random matrix models of disordered bosons
摘要：
无序玻色子的随机矩阵模型由李代数g=sp_n（R）中的矩阵组成。假设动力学稳定，它们的特征值必须是纯虚的。在这里，提出了一种方法，用于构建系综（E，P）的G-不变集E这样的矩阵的概率措施P。这些出现作为矩映射直接图像从相空间X中发挥重要作用，在复杂的几何和表示理论。在n=1的Toy模型情形下，给出了谱测度的一个显式描述，其中X是复双圆盘，P是一致测度的直像.
英文摘要：
Random matrix models of disordered bosons consist of matrices in the Lie algebra g=sp_n(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary. Here a method is proposed for constructing ensembles (E,P) of G-invariant sets E of such matrices with probability measures P. These arise as moment map direct images from phase spaces X which play an important role in complex geometry and representation theory. In the toy-model case of n=1, where X is the complex bidisk and P is the direct image of the uniform measure, an explicit description of the spectral measure is given.
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