Dynamics of microscale and nanoscale systems in the weak-memory regime

Brandner, Kay

Abstract

Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are nonlocal in time. If the characteristic timescales of accessible and inaccessible degrees of freedom are sharply separated, locality can be restored through the standard Markov approximation. Here, we show that this approach can be rigorously extended to a well-defined weak-memory regime, where the relevant timescales can be of comparable order of magnitude. We derive explicit bounds on the error of the local approximation and a convergent perturbation scheme for its construction. Being applicable to any nonlocal time evolution equation that is autonomous and linear in the variables of interest, our theory provides a unifying framework for the systematic description of memory effects.

Citation

Brandner, K. (2025). Dynamics of microscale and nanoscale systems in the weak-memory regime. Physical Review Letters, 134(3), Article 037401. https://doi.org/10.1103/physrevlett.134.037101

• Journal Article Type: Article
• Acceptance Date: Dec 2, 2024
• Online Publication Date: Jan 21, 2025
• Publication Date: Jan 24, 2025
• Deposit Date: Apr 15, 2025
• Publicly Available Date: Apr 15, 2025
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 134
• Issue: 3
• Article Number: 037401
• DOI: https://doi.org/10.1103/physrevlett.134.037101
• Public URL: https://nottingham-repository.worktribe.com/output/47822967
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.037101