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Optimal sampling of dynamical large deviations via matrix product states

Causer, Luke; Bañuls, Mari Carmen; Garrahan, Juan P.

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Authors

Luke Causer

Mari Carmen Bañuls



Abstract

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions.

Citation

Causer, L., Bañuls, M. C., & Garrahan, J. P. (2021). Optimal sampling of dynamical large deviations via matrix product states. Physical Review E, 103(6), Article 062144. https://doi.org/10.1103/PhysRevE.103.062144

Journal Article Type Article
Acceptance Date May 7, 2021
Online Publication Date Jun 28, 2021
Publication Date Jun 1, 2021
Deposit Date Jul 22, 2021
Publicly Available Date Mar 29, 2024
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 2470-0053
Peer Reviewed Peer Reviewed
Volume 103
Issue 6
Article Number 062144
DOI https://doi.org/10.1103/PhysRevE.103.062144
Public URL https://nottingham-repository.worktribe.com/output/5814895
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.062144
Additional Information ©2021 American Physical Society

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