Universal Spectral Statistics in Quantum Graphs
β Scribed by Gnutzmann, Sven; Altland, Alexander
- Book ID
- 119948255
- Publisher
- The American Physical Society
- Year
- 2004
- Tongue
- English
- Weight
- 122 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0031-9007
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the graphs, where the dynamics is mixing and the periodic orbits
We study the spectral determinant of the Laplacian on finite graphs characterized by their number of vertices V and bonds B. We present a path integral derivation which leads to two equivalent expressions of the spectral determinant of the Laplacian in terms of either a V\_V vertex matrix or a 2B\_2