Krylov complexity and orthogonal polynomials

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 poly...

Full description

Saved in:

Bibliographic Details
Published in:	arXiv.org
Main Authors:	Mück, Wolfgang, Yang, Yi
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 25.05.2022
Subjects:	Algorithms Complexity Mathematical analysis Polynomials
ISSN:	2331-8422
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2205.12815