| EPSRC Reference: |
GR/N01415/01 |
| Title: |
SCHRODINGER TYPE EQUATIONS WITH SINGULAR RANDOM COEFFICIENTS AND PATH INTEGRAL METHODS |
| Principal Investigator: |
Truman, Professor A |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Swansea University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
13 November 1999 |
Ends: |
12 May 2000 |
Value (£): |
5,500
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The VF, in collaboration with the investigator will undertake the study of Schrodinger, Bloch and related equations with singular random co-efficient of Poisson and Gaussian type by analytic continuation of Wiener and Poisson type stochastic integrals in infinite dimensional spaces. Relationships between holomorphic, phase, momentum and configuration path integral representations of the solutions to these equations will be established and a non-cummative generalisation to the quantum stochastic equations for open systems will be sought. Asymptotical solutions to the stochastic and quantum stochastic equations in quasi-classical approximation will be studied by the Maslov-Hormander method as well as their numerical simulations. The non-commutative Cameron-Martin-Girsanov transformation and Feynman-Kac formula is expected to be established in the stochastic case which will open several fruitful directions to be followed by the participants in their future research projects.
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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.swan.ac.uk |