Form factor for a family of quantum graphs: An expansion to third order
| dc.creator | Berkolaiko, Gregory | |
| dc.creator | Schanz, Holger | |
| dc.creator | Whitney, Robert S. | |
| dc.date | 2002-05-08 | |
| dc.date | 2003-06-30 | |
| dc.date.accessioned | 2026-07-07T06:27:37Z | |
| dc.date.available | 2026-07-07T06:27:37Z | |
| dc.description | 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 $τ$ 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-$τ$ contribution, the diagonal approximation, already reproduces the random-matrix form factor for $τ<1$. For systems with time-reversal symmetry there are more diagrams which contribute at third order. We sum these contributions for quantum graphs with uniformly hyperbolic dynamics, obtaining $+2τ^{3}$, in agreement with random-matrix theory. As in the previous calculation of the leading-order correction to the diagonal approximation we find that the third order contribution can be attributed to exceptional orbits representing the intersection of diagram classes. | |
| dc.description | 23 pages (including 4 fig.) - numerous typos corrected | |
| dc.identifier | https://arxiv.org/abs/nlin/0205014 | |
| dc.identifier | http://arxiv.org/abs/nlin/0205014 | |
| dc.identifier | J. Phys. A 36 8373-8392 (2003) | |
| dc.identifier | doi:10.1088/0305-4470/36/31/303 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97461 | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.title | Form factor for a family of quantum graphs: An expansion to third order | |
| dc.type | text |