| EPSRC Reference: |
GR/R67279/01 |
| Title: |
Semiclassical dynamics of nonuniformaly hyperbolic maps: localization versus quantum ergodicity |
| Principal Investigator: |
Marklof, Professor J |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Fast Stream |
| Starts: |
01 October 2001 |
Ends: |
30 September 2004 |
Value (£): |
56,145
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
One of the central aspects of the theory of quantum chaos is concerned with the semiclassical distribution of quantum eigenmodes. It is known that if the underlying classical dynamics is ergodic, almost all eigenmodes become equidistributed in the available classical phase space. The question as to whether in fact all eigenmodes become equidistributed is currently highly controversial. There are only a few systems known where quantum unique ergodicity (i.e., the equidistribution of eigenmodes) can be proved on a rigorous basis; on the other hand, exceptional sequences of localized eigenmodes ( scars , bouncing ball modes ) have been observed in numerical experiments, e.g., with stadium-shaped quantum billiards. An essential feature of systems with exceptional eigenmodes is the highly nonuniform hyperbolicity of the underlying classical dynamics. The main objective of the research programme is to give a first proof of the existence of such localized states in certain quantized maps of the torus, whose dynamical properties are similar to the more complicated billiard systems where scarred eigenmodes have been observed numerically.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.bris.ac.uk |