Generalized Krylov Complexity
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916895142182912 |
|---|---|
| author | Astaneh, Amin Faraji Vardian, Niloofar |
| author_facet | Astaneh, Amin Faraji Vardian, Niloofar |
| contents | We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the complexity of states associated with continuous symmetries within a model. Furthermore, we investigate scenarios where different directions of transformation lead to varying degrees of complexity, which can be compared to geometric approaches to understanding complexity, such as Nielsen complexity. In this context, we introduce a generalized orthogonalization algorithm and delineate its computational framework, which is structured as a network of orthogonal blocks rather than a simple linear chain. Additionally, we provide explicit evaluations of specific illustrative examples to demonstrate the practical application of this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Krylov Complexity Astaneh, Amin Faraji Vardian, Niloofar High Energy Physics - Theory Quantum Physics We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the complexity of states associated with continuous symmetries within a model. Furthermore, we investigate scenarios where different directions of transformation lead to varying degrees of complexity, which can be compared to geometric approaches to understanding complexity, such as Nielsen complexity. In this context, we introduce a generalized orthogonalization algorithm and delineate its computational framework, which is structured as a network of orthogonal blocks rather than a simple linear chain. Additionally, we provide explicit evaluations of specific illustrative examples to demonstrate the practical application of this framework. |
| title | Generalized Krylov Complexity |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2507.23739 |