Quantum graphs: Applications to quantum chaos and universal spectral statistics
By Sven Gnutzmann∥, Uzy Smilansky. 2006
340 citations recorded by the source corpus.
During the last few years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wavefunction statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. In particular, we summarize recent developments on the spectral statistics of generic large quantum graphs based on two approaches: the periodic-orbit approach and the supersymmetry approach. The latter provides a condition and a proof for universal spectral statistics as predicted by random-matrix theory.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/cc6f048ecf544bbdeaaab0bc2df1d1611e41a277
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “It is surveyed in [109], as well as in [124] in [77].”
- Bound states of the NLS equation on metric graphs with localized nonlinearities (2015, background): “Driven by the applications, the study of dynamics on quantum graphs has gained popularity in recent years since graphs emulate accurately complex mesoscopic and optical networks and allow one to reproduce properties of quantum chaotic systems (see [15, 18]).”