Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy and Generalized Hydrodynamics

Bertini, Bruno; Essler, Fabian H. L.; Granet, Etienne

Abstract

We consider fermions defined on a continuous one-dimensional interval and subject to weak repulsive two-body interactions. We show that it is possible to perturbatively construct an extensive number of mutually compatible conserved charges for any interaction potential. However, the contributions to the densities of these charges at second order and higher are generally nonlocal and become spatially localized only if the potential fulfils certain compatibility conditions. We prove that the only solutions to the first of these conditions are the Cheon-Shigehara potential (fermionic dual to the Lieb-Liniger model) and the Calogero-Sutherland potentials. We use our construction to show how generalized hydrodynamics emerges from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and argue that generalized hydrodynamics in the weak interaction regime is robust under nonintegrable perturbations.

Citation

Bertini, B., Essler, F. H., & Granet, E. (2022). Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy and Generalized Hydrodynamics. Physical Review Letters, 128(19), Article 190401. https://doi.org/10.1103/PhysRevLett.128.190401

• Journal Article Type: Article
• Acceptance Date: Apr 5, 2022
• Online Publication Date: May 12, 2022
• Publication Date: May 13, 2022
• Deposit Date: Jun 14, 2022
• Publicly Available Date: Jun 20, 2022
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 128
• Issue: 19
• Article Number: 190401
• DOI: https://doi.org/10.1103/PhysRevLett.128.190401
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/8496449
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.190401