| EPSRC Reference: |
GR/T28058/01 |
| Title: |
Long Time Limit of Chaotic Quantum Dynamics |
| Principal Investigator: |
Marklof, Professor J |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2005 |
Ends: |
31 March 2008 |
Value (£): |
156,373
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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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The proposed research project aims to solve one of the most challenging problems in quantum chaos: the long-time evolution of an initially localized wavepacket for quantum systems whose underlying classical dynamics is strongly chaotic.It is well known that for sufficiently high frequencies the propagation of wave fronts is driven by the trajectories of an underlying classical dynamical system. In electromagnetism this underlying classical system is described by the ray dynamics in geometrical optics, in quantum mechanics it is the classical Hamiltonian mechanics emerging in the semiclassical limit, and in the general theory of hyperbolic partial differential equations the underlying system is the bicharacteristic flow.The ergodic properties of the underlying dynamics are therfore expected to determine the pattern of the waves for large times. Especially if the dynamics is chaotic we expect the emerging patterns to be universal and random. It is the principal objective of the proposed research project to prove such a behaviour rigorously. This key result would establish several important and long standing conjectures on long-time quantum dynamics published in the Physics and Chemistry literature and open up a new field of research on qualitative behaviour of wave propagation.
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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.bris.ac.uk |