| EPSRC Reference: |
GR/T19117/01 |
| Title: |
Pair correlations of length spectra, quantum chaos and thermodynamic formalism |
| Principal Investigator: |
Pollicott, Professor M |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 March 2005 |
Ends: |
29 February 2008 |
Value (£): |
139,180
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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One of the most exciting interdisciplinary fields to emerge in recent years is at the intersection of three of the most important and active research areas in Mathematics: Number Theory, Geometry and Mathematical Physics. One goal in this theory, Quantum Chaos, is to understand from a geometric vantage point certain natural analytically defined characteristics (eigenvalues of the Laplacian) associated to manifolds. A very fruitful approach is to study the intimately related set of values given by the lengths of closed geodesics. In particular, by interpreting these as closed orbits of an associated dynamical system (the geodesic flow) we can bring to bear many powerful tools from ergodic theory and the general theory of dynamical systems. More precisely, important aspects of the spectral theory and Quantum Chaos, such as pair correlation's and the determinant of the Laplacian are amenable to study using symbolic dynamics and Thermodynamic Formalism.
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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 |
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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.warwick.ac.uk |