Quantum Dynamics in Krylov Space: Methods and Applications

Quantum Physics; Physics - Statistical Mechanics; Physics - Strongly Correlated Electrons; High Energy Physics - Theory; Nonlinear Sciences - Chaotic Dynamics

Abstract :

[en] The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide an efficient description of quantum evolution and quantum chaos, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems.

Disciplines :

Physics

Author, co-author :

NANDY, Pratik ; University of Luxembourg

MATSOUKAS, Stylianos Apollonas ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Adolfo DEL CAMPO ECHEVARRIA

MARTINEZ AZCONA, Pablo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

Dymarsky, Anatoly

DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg

External co-authors :

yes

Language :

English

Title :

Quantum Dynamics in Krylov Space: Methods and Applications

Publication date :

2024

Journal title :

Physics Reports

ISSN :

0370-1573

Publisher :

Elsevier BV

Volume :

1125-1128

Pages :

1-82

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0370157325001462?httpAccept=text/xml

Funders :

Japan Society for the Promotion of Science
National Research Fund

Commentary :

Invited review article in Physics Reports, v3: few sections added, typos corrected, refs added. Published version in Physics Reports

Available on ORBilu :

since 20 May 2025

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362 (3 by Unilu)

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