论文标题
可溶解的随机矩阵合奏，具有对数弱限制电势
Solvable random matrix ensemble with a logarithmic weakly confining potential
论文作者
论文摘要
这项工作确定了可解决的方法（从某种意义上说，光谱相关函数可以用正交多项式来表示），旋转不变的随机矩阵集合集合具有对数弱限制的潜力。可以将其解释为转化的雅各比集合的合奏在以洛伦兹特征值密度为特征的热力学极限中。结果表明，光谱相关函数可以用非经典的gegenbauer多项式来表示，$ c_n^{（ - 1/2）}（x）$带有$ n \ ge 2 $，已被证明可以与适当的重量函数相关地形成完整的正交设置。概述了从集合中采样矩阵的程序，并用于为某些分析结果提供数值验证。指出该合奏有可能在量子多体物理学中应用。
This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The ensemble, which can be interpreted as a transformed Jacobi ensemble, is in the thermodynamic limit characterized by a Lorentzian eigenvalue density. It is shown that spectral correlation functions can be expressed in terms of the nonclassical Gegenbauer polynomials $C_n^{(-1/2)}(x)$ with $n \ge 2$, which have been proven to form a complete orthogonal set with respect to the proper weight function. A procedure to sample matrices from the ensemble is outlined and used to provide a numerical verification for some of the analytical results. This ensemble is pointed out to potentially have applications in quantum many-body physics.
