| EPSRC Reference: |
GR/S57099/01 |
| Title: |
Eo-semigroups & quantum stochastic dilations |
| Principal Investigator: |
Lindsay, Professor JM |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
University of Nottingham |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2003 |
Ends: |
30 June 2003 |
Value (£): |
4,500
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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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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The two fields of Eo-semigroup theory and quantum stochastic calculus have seen significant independent progress over the last few years. The proposed VF and investigator have been at the forefront respectively of the former and the latter. Moreover the VF has begun to link the two. A research collaboration to discover their deeper connections, applying stochastic calculus to the Eo-theory and classification ideas from Eo-theory to quantum stochastic dilations is therefore timely. This new collaboration is in a long line of successful collaborations between Nottingham and ISImathematicians.The proposal is specifically to find the product structure of Eo-semigroups arising from dilations of quantum dynamical semigroups via quantum stochastic calculus, with a view to classifying them; to investigate minimality of these dilations and the relationship of nonminimal to minimal dilations; and more speculatively, to explore the possibilities of devising stochastic calculus for the infinitesimal analysis of a wider class (non-Type I) of Eosemigroups. Time-ordered Fock modules provide promising candidates for the product structure of QS dilations. Minimality for QS dilations first needs a good definition, then existence should be established, and we would seek to characterise minimality in terms of the OS generator of thedilation.
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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.nottingham.ac.uk |