Details of Grant 

EPSRC Reference:	GR/A10772/01
Title:	EQUIDISTRIBUTION, EXPONENTIAL SUMS AND QUANTUM CHAOS
Principal Investigator:	Marklof, Professor J
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Bristol
Scheme:	Advanced Fellowship (Pre-FEC)
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:	Communications
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 (Berry-Tabor conjecture). If the dynamics is chaotic, the statistics should be modelled by suitable random matrix ensembles (Bohigas-Giannoni-Schmit conjecture). The Berry-Tabor 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 n-point 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 Bohigas-Giannoni-Schmit 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.
Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk Summary Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:
Further Information:
Organisation Website:	http://www.bris.ac.uk