| EPSRC Reference: |
GR/S79633/01 |
| Title: |
Number-Theoretic Aspects of Quantum Chaos |
| Principal Investigator: |
Marklof, Professor J |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 July 2004 |
Ends: |
30 September 2004 |
Value (£): |
10,199
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
| Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Describe the proposed research using (about 200) words geared to the non-specialist reader.One of the fundamental problems in the theory of quantum chaos is to identify universal statistical properties of quantum systems. The proposed project will investigate special classes of systems, where these questions can be attacked with number-theoretic techniques. We focus on (i) the proof of a central limit theorem for fluctuation of energy levels and (ii) the distribution of quantum eigenstates.The first objective (i) will be studied for the eigenvalues of the Laplacian of a flat torus, which are given by values of quadratic forms at lattice points, and the modular surface. The second objective (ii) looks at eigenstates of quantized linear automorphisms of the torus, which leads to questions on the distribution of certain exponential sums. We will also investigate the connection between random matrix theory and L-functions, and attempt to prove that the value distribution of families of L-functions taken at the centre of the critical strip satisfies a central limit theorem.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bris.ac.uk |