Number Theory Related to Quantum Chaos and Dynamics

Project funded by Swedish Research Council (Project grant), grant 2024-04820_VR. Participating organisations named by the source: KTH, Royal Institute of Technology. Funded amount: SEK 4,080,000, as stated by the source. Runs 2025-01-01 to 2028-12-31. Keywords: Oklassificerat, Unclassified. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-04); national funding data, not CORDIS. Abstract given by the source: The goal is to study number theoretical questions related to mathematical physics and dynamical systems, and prove or disprove conjectures by the physics community. Quantum Chaos is concerned with how chaos in classical systems manifests itself in terms of quantum mechanics, e.g. can chaos be detected in the statistical behavior of the gaps between eigenvalues ("energy levels") of quantized Hamiltonians? Pursuing this question for some arithmetic systems leads to intriguing questions regarding "deterministic randomness" - even though the eigenvalues are determined by simple rules, in many ways it behaves as a truly random sequence. Another question is properties of eigenfunctions of quantized Hamiltonians. For ergodic classical dynamics, most eigenfunctions should be equidistributed in a certain sense. Other "fingerprints of chaos" is the distribution of zero sets ("nodal lines") of eigenfunctions, to be compared with predictions given by Berry´s Random Wave model for chaotic eigenfunctions. An interesting class of models is given by Laplace eigenfunctions on tori when perturbed by delta potentials; the aritmetic nature of the unperturbed Laplace multiplicities gives rise to subtle and interesting number theoretical questions. The research consists of several subprojects that will be carried out by the PI and a student or postdoc.Rigorous proof of level repulsion, or validy of Berry´s random wave model for deterministic eigenfunctions, would be major breakthroughs.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Number Theory Related to Quantum Chaos and Dynamics" is funded by the Swedish Research Council with a grant of SEK 4,080,000, running from January 1, 2025, to December 31, 2028. It aims to explore number theoretical questions in mathematical physics and dynamical systems. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.