```
Gnutzmann, Sven, Altland, Alexander, and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne.
```*Spectral correlations of individual quantum graphs*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevE.72.056215.

```
Gnutzmann, Sven, Altland, Alexander, & Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne.
```*Spectral correlations of individual quantum graphs*. United States. doi:10.1103/PhysRevE.72.056215.

```
Gnutzmann, Sven, Altland, Alexander, and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne. Tue .
"Spectral correlations of individual quantum graphs". United States.
doi:10.1103/PhysRevE.72.056215.
```

```
@article{osti_20709843,
```

title = {Spectral correlations of individual quantum graphs},

author = {Gnutzmann, Sven and Altland, Alexander and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne},

abstractNote = {We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear {sigma}-model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.},

doi = {10.1103/PhysRevE.72.056215},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}