EPSRC Reference: 
GR/A10772/01 
Title: 
EQUIDISTRIBUTION, EXPONENTIAL SUMS AND QUANTUM CHAOS 
Principal Investigator: 
Marklof, Professor J 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Bristol 
Scheme: 
Advanced Fellowship (PreFEC) 
Starts: 
01 October 2001 
Ends: 
30 September 2006 
Value (£): 
214,591

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


EPSRC Industrial Sector Classifications: 

Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
16 Nov 2000

Maths Advanced/Senior Fellowship Sifting Panel

Deferred


Summary on Grant Application Form 
The theory of quantum chaos is concerned with statistical properties of quantum systems which mirror the ergodic properties of the underlying classical dynamics. If the classical dynamics is completely integrable, the correlations are expected to be those of a Poisson process (BerryTabor conjecture). If the dynamics is chaotic, the statistics should be modelled by suitable random matrix ensembles (BohigasGiannoniSchmit conjecture). The BerryTabor conjecture leads to subtle equidistribution problems for the values of homogeneous functions at lattice points. The main part of the project will first focus on extending my present techniques, valid for pair correlation densities of binary quadratic forms, to forms in more variables and higher npoint correlations. This will involve the theory of exponential theta sums and equidistribution of unipotent orbits on Lie groups. The results may then be extended to more general functions homogeneous of degree two. The second part of the project is expected to shed more light on the truth of the BohigasGiannoniSchmit conjecture for simple models such as geodesic flows on hyperbolic manifolds, symplectic maps and graphs. A third aspect of the project is concerned with the question of quantum unique ergodicity and existence of localized eigenmodes ( scars ) in quantum systems with ergodic classical limit.

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Further Information: 

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