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Title: PT-symmetric quantum chaos and random matrix theory
Author: Mudute-Ndumbe, Steve
ISNI:       0000 0004 8504 6795
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2019
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In this thesis we investigate the intersection of the three fields of random matrix theory, quantum chaos, and PT-symmetric quantum mechanics. The thesis is split into two Parts. The first Part is devoted to random matrix theory, where we first recap some spectral properties of the well-known Gaussian and Ginibre random matrix ensembles. We then introduce some new PT-symmetric random matrix ensembles, exploring the features of their eigenvalues, and discover that one of these new ensembles is spectrally equivalent to one of the existing Ginibre ensembles, whilst to our knowledge the other has no relation with any other existing ensemble. In the second Part, we look at two popular models in quantum chaos known as the baker map and the kicked top, and explore PT-symmetric extensions of them. For the PT-symmetric kicked top we observe new types of classical dynamics where despite the non-Hamiltonian form of the dynamics there are no attractors in the non-chaotic regime, while we observe what appears to be a strange attractor in the deep chaotic regime for even small non-Hermitian parameters. We can observe fingerprints of the classical structures in the quantum Floquet states. Finally, we find similar characteristics in the spectral features of the PT-symmetric versions of both the kicked top and the baker map. These results open the door for myriad avenues to further pursue.
Supervisor: Graefe, Eva-Maria ; Krasovsky, Igor Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral