Deterministic many-body dynamics with multifractal response

Kasim, Yusuf (author), Prosen, Tomaž (author)

Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of nonergodic behavior in a many-body discrete-time dynamical system, specifically a multiperiodic response with multifractal distribution of equilibrium spectral weights at all rational frequencies. This phenomenon is observed in the momentum-conserving variant of the newly introduced class of the so-called parity check reversible cellular automata, which we define with respect to an arbitrary bipartite lattice. Although the models display strong fragmentation of phase space of configurations, we demonstrate that the effect qualitatively persists within individual fragmented sectors, and even individual typical many-body trajectories. We provide detailed numerical analysis of examples on 2D (honeycomb, square) and 3D (cubic) lattices.

• Language: English
• Keywords: celular automata, ergodicity, lattice models
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 023230-1-023230-11
• Numbering: Vol. 7, iss. 2
• PID: 20.500.12556/RUL-175243
• UDC: 536.9
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.7.023230
• COBISS.SI-ID: 254355203
• Publication date in RUL: 22.10.2025

Record is a part of a journal

• Title: Physical review research
• Publisher: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: celični avtomati, ergodičnost, modeli na mreži