Number Theory Related to Quantum Chaos and Dynamics

Project funded by Swedish Research Council (Project grant), grant 2016-03701_VR. Participating organisations named by the source: KTH, Royal Institute of Technology. Funded amount: SEK 2,800,000, as stated by the source. Runs 2017-01-01 to 2020-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Annan matematik, Other Mathematics. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-06); national funding data, not CORDIS. Abstract given by the source: The goal of this project is to study some number theoretical questions related to mathematical physics and dynamical systems. Quantum Chaos is concerned with how chaos in classical systems manifests itself in terms of quantum mechanics. For instance, can chaos be detected in the statistical behavior of the gaps between eigenvalues (which can be interpreted as energy levels) of so-called quantized Hamiltonians? Pursuing this question for some integrable systems leads to some intriguing questions regarding "deterministic randomness” - even though the sequence of eigenvalues is determined by simple rules, in many ways it behaves very much as a truly random sequence. Also worth noting is that the distribution of gaps (or so-called level-correlations), is a very natural refinement of the notion of equidistribution of a sequence.Another question is properties of eigenfunctions of quantized Hamiltonians. If the classical dynamics are ergodic, then 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, in particular when perturbed by delta potentials (”Seba billiards”); the aritmetic nature of the (unperturbed) Laplace multiplicities gives rise to some very subtle and interesting number theoretical questions.

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: This project, funded by the Swedish Research Council (grant 2016-03701_VR) for SEK 2,800,000, ran from 2017-01-01 to 2020-12-31. It studied number theory questions related to mathematical physics and dynamical systems, specifically quantum chaos and the statistical behavior of eigenvalue gaps. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.