论文标题
随机分割的三角形准t-toeplitz矩阵的封闭形式的特征值：随机驱动块共聚物
Closed form Eigenvalues of Randomly Segmented Tridiagonal quasi-Toeplitz Matrices: Random Rouse block copolymer
论文作者
论文摘要
我们以精确的闭合形式计算一类随机矩阵的特征值，即随机分割的三角形准to-toeplitz（RSTQ-T）矩阵。这些矩阵出现的上下文在物理学中无处不在。在我们的情况下，它们在研究嵌入随机环境中的Rouse聚合物的动力学时会产生。与均匀环境中的鲁斯聚合物不同，动力学产生循环基质，并且通过傅立叶变换很容易实现对角线化，迄今为止，RSTQ-T矩阵的分析对角线已经无法解决。我们通过分析计算RSTQ-T矩阵的光谱分布，该矩阵能够捕获障碍对模式的影响。
We calculate the eigenvalues of a class of random matrices, namely the randomly segmented tridiagonal quasi-Toeplitz (rstq-T) matrix, in exact closed-form. The contexts under which these matrices arise are ubiquitous in physics. In our case, they arise when studying the dynamics of a Rouse polymer embedded in random environments. Unlike in the case of Rouse polymers in homogeneous environments, where the dynamics give rise to a circulant matrix and the diagonalization is achieved easily via a Fourier transform, analytical diagonalization of the rstq-T matrix has remained unsolved thus far. We analytically calculate the spectral distribution of the rstq-T matrix, which is able to capture the effect of disorder on the modes.
