| Автор | Gregor Tanner |
| Дата выпуска | 2000-05-12 |
| dc.description | Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalize this approach by considering arbitrary, directed graphs with unitary transfer matrices. An exponentially increasing contribution to the form factor is identified when performing a diagonal summation over periodic orbit degeneracy classes. A special class of graphs, so-called binary graphs, is studied in more detail. For these, the conditions for periodic orbit pairs to be correlated (including correlations due to the unitarity of the transfer matrix) can be given explicitly. Using combinatorial techniques it is possible to perform the summation over correlated periodic orbit pair contributions to the form factor for some low-dimensional cases. Gradual convergence towards random matrix results is observed when increasing the number of vertices of the binary graphs. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Spectral statistics for unitary transfer matrices of binary graphs |
| Тип | paper |
| DOI | 10.1088/0305-4470/33/18/304 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 33 |
| Первая страница | 3567 |
| Последняя страница | 3585 |
| Аффилиация | Gregor Tanner; School of Mathematical Sciences, Division of Theoretical Mechanics, University of Nottingham, University Park, Nottingham NG7 2RD, UK |
| Выпуск | 18 |
