Charlie Johnson

Generalised Time-Reversal Symmetries on Quantum Graphs

A major result of quantum chaos is that energy level sub spectra of chaotic systems correspond to random matrix ensembles. Furthermore, these ensembles can be completely determined by studying the symmetries of the system, of both unitary (geometric) and anti-unitary (time-reversal) type. It is then useful to be able to construct systems with arbitrary unitary and anti-unitary symmetries to test the random matrix theory ensembles. Quantum Graphs have typically been used for this purpose, but they have so far been restricted to containing only a simple complex-conjugation time-reversal symmetry, or completely broken time-reversal symmetry. We demonstrate how to generate graphs with generalised time-reversal symmetries, combining complex-conjugation with a unitary component, and show these graphs fulfil their random matrix theory predictions.