Form factor for a family of quantum graphs: an expansion to third order
| Autor: | Gregory Berkolaiko, Robert S. Whitney, Holger Schanz |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Condensed Matter - Mesoscale and Nanoscale Physics
Diagonal Diagram Form factor (quantum field theory) FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Nonlinear Sciences - Chaotic Dynamics Third order Intersection Quantum graph Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Ergodic theory Chaotic Dynamics (nlin.CD) Symmetry (geometry) Mathematical Physics Mathematics Mathematical physics |
| Zdroj: | Journal of Physics A: Mathematical and General. 36:8373-8392 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/36/31/303 |
| Popis: | For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits represented by diagrams with up to two self-intersections connected by up to four arcs and explain why all other diagrams are expected to give higher-order corrections only. For a large family of graphs with ergodic classical dynamics the diagrams that exist in the absence of time-reversal symmetry sum to zero. The mechanism for this cancellation is rather general which suggests that it may also apply at higher-orders in the expansion. This expectation is in full agreement with the fact that in this case the linear-$\tau$ contribution, the diagonal approximation, already reproduces the random-matrix form factor for $\tau Comment: 23 pages (including 4 fig.) - numerous typos corrected |
| Databáze: | OpenAIRE |
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