EPSRC Reference: 
GR/R13838/01 
Title: 
Random Matrices Close To Unitary Or Hermitian and Scattering Theory For Systems With Quantum Chaos 
Principal Investigator: 
Fyodorov, Professor Y 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Sciences 
Organisation: 
Brunel University London 
Scheme: 
Fast Stream 
Starts: 
01 June 2001 
Ends: 
30 November 2002 
Value (£): 
61,576

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
We will 1) calculate multipoint correlation functions of products and ratios of spectral determinants for large nonHermitian random matrices exploting the mapping onto a nonlinear sigmamodel. We will try also to get insights into related problems for complex symmetric matrices 2) calculate the twopoint correlation function of spectral determinants of nonunitary random matrices of arbitrary size using ItzyksonZuberHarishChandra integral and express it in terms of symmetric polynomials. Further, we will try to calculate correlation functions of traces of integer powers of nonunitary matrices which can be instructive for revealing the underlying combinatorial structures. 3) use the obtained correlation functions for extracting statistical information on eigenvalues and eigenvectors, as well as on elements of Smatrix, crosssections and other characteristics of quantum chaotic scattering. 4) consider lowrank perturbations of large random matrices from point of view of possible relations to integrable models of CalogeroSutherland type. 1) We will calculate multipoint correlation functions of products and ratios of spectral determinants for large nonHermitian random matrices exploting the mapping onto a nonlinear sigmamodel. We will try also to get insights into related problems for complex symmetric matrices.2) Calculate the twopoint correlation function of spectral determinants of nonunitary random matrices of arbitrary size using ItzyksonZuberHarishChandra integral and express it in terms of symmetric polynomials. Further, we will try to calculate correlation functions of traces of integer powers of nonunitary matrices which can be instructive for revealing the underlying combinatorial structures.3) Use the obtained correlation functions for extracting statistical information on eigenvalues and eigenvectors, as well as on elements of Smatrix, crosssections and other characteristics of quantum chaotic scattering.4) Consider lowrank perturbations of large random matrices for point of view of possible relations to integrable models of calogeroSutherland type.

Key Findings 
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Organisation Website: 
http://www.brunel.ac.uk 