Number Theory Related to Quantum Chaos and Dynamics

Project funded by Swedish Research Council (Project grant), grant 2011-05498_VR. Participating organisations named by the source: KTH, Royal Institute of Technology. Funded amount: SEK 4,050,000, as stated by the source. Runs 2012-01-01 to 2015-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Matematisk analys, Mathematical Analysis. 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: In this project, I will 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, or lack thereof, 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, often with number theoretical "flavor", in many ways it behaves very much as a truly random sequence. Also worth noting is that the distribution of gaps, and also the so-called level-correlations, can be viewed as 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. Arnold´s "cat map" is a simple model of a chaotic system, whose arithmetical features makes it possible to prove rather strong forms of equidistribution, as well as determining the value distribution of eigenfunctions (for restricted values of Planck´s constant.) I intend to determine the value distribution for general values of Planck´s constant.

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" was funded by the Swedish Research Council with a grant of SEK 4,050,000, running from January 1, 2012, to December 31, 2015, involving KTH, Royal Institute of Technology. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.