论文标题
Krylov的复杂性和正交多项式
Krylov complexity and orthogonal polynomials
论文作者
论文摘要
Krylov的复杂性测量了操作员相对于基础的增长，这适用于海森堡时间的演变。该基础的构建依赖于兰开斯算法，也称为递归法。可以用正交多项式来描述Krylov复杂性的数学。我们提供了对该主题的教学介绍，并在分析上进行了许多涉及经典正交多项式，Hahn类别的多项式和Tricomi-Carlitz多项式的示例。
Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method. The mathematics of Krylov complexity can be described in terms of orthogonal polynomials. We provide a pedagogical introduction to the subject and work out analytically a number of examples involving the classical orthogonal polynomials, polynomials of the Hahn class, and the Tricomi-Carlitz polynomials.
