Statistics of the spectral form factor in the self-dual kicked Ising model

Flack, Ana (author), Bertini, Bruno (author), Prosen, Tomaž (author)

We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at long enough times the probability distribution agrees exactly with the prediction of random-matrix theory if one identifies the appropriate ensemble of random matrices. We find that this ensemble is not the circular orthogonal one—composed of symmetric random unitary matrices and associated with time-reversal-invariant evolution operators—but is an ensemble of random matrices on a more restricted symmetric space [depending on the parity of the number of sites this space is either S p(N)/U (N) or O(2N)/O(N)×O(N)]. Even if the latter ensembles yield the same averaged spectral form factor as the circular orthogonal ensemble, they show substantially enhanced fluctuations. This behavior is due to a recently identified additional antiunitary symmetry of the self-dual kicked Ising model.

• Language: English
• Keywords: statistical physics, quantum chaos
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2020
• Number of pages: Str. 043403-1-043403-14
• Numbering: Vol. 2, iss. 4
• PID: 20.500.12556/RUL-124534
• UDC: 536
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.2.043403
• COBISS.SI-ID: 49281539
• Publication date in RUL: 29.01.2021

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.
• Licensing start date: 29.01.2021

Secondary language

• Language: Slovenian
• Keywords: statističma fizika, kvantni kaos

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika