| 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: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematical Sciences |
| Organisation: |
Brunel University London |
| Scheme: |
Fast Stream |
| Starts: |
01 June 2001 |
Ends: |
30 November 2002 |
Value (£): |
61,576
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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We will 1) calculate multipoint correlation functions of products and ratios of spectral determinants for large non-Hermitian random matrices exploting the mapping onto a non-linear sigma-model. We will try also to get insights into related problems for complex symmetric matrices 2) calculate the two-point correlation function of spectral determinants of non-unitary random matrices of arbitrary size using Itzykson-Zuber-Harish-Chandra integral and express it in terms of symmetric polynomials. Further, we will try to calculate correlation functions of traces of integer powers of non-unitary 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 S-matrix, cross-sections and other characteristics of quantum chaotic scattering. 4) consider low-rank perturbations of large random matrices from point of view of possible relations to integrable models of Calogero-Sutherland type. 1) We will calculate multipoint correlation functions of products and ratios of spectral determinants for large non-Hermitian random matrices exploting the mapping onto a non-linear sigma-model. We will try also to get insights into related problems for complex symmetric matrices.2) Calculate the two-point correlation function of spectral determinants of non-unitary random matrices of arbitrary size using Itzykson-Zuber-Harish-Chandra integral and express it in terms of symmetric polynomials. Further, we will try to calculate correlation functions of traces of integer powers of non-unitary 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 S-matrix, cross-sections and other characteristics of quantum chaotic scattering.4) Consider low-rank perturbations of large random matrices for point of view of possible relations to integrable models of calogero-Sutherland type.
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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.brunel.ac.uk |