EPSRC Reference: 
GR/S79633/01 
Title: 
NumberTheoretic Aspects of Quantum Chaos 
Principal Investigator: 
Marklof, Professor J 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Bristol 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 July 2004 
Ends: 
30 September 2004 
Value (£): 
10,199

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Analysis 
Mathematical Physics 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Describe the proposed research using (about 200) words geared to the nonspecialist 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 numbertheoretic 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 Lfunctions, and attempt to prove that the value distribution of families of Lfunctions taken at the centre of the critical strip satisfies a central limit theorem.

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Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.bris.ac.uk 