Quantum chaos in a non-Hermitian PT-symmetric kicked top
File(s)
Published version
Author(s)
Mudute-Ndumbe, Steve
Graefe, Eva-Maria
Type
Journal Article
Abstract
A non-Hermitian PT-symmetric version of the kicked top is introduced to study the interplay of quantum chaos with balanced loss and gain. The classical dynamics arising from the quantum dynamics of the angular momentum expectation values are derived. It is demonstrated that the presence of PT-symmetry can lead to 'stable' mixed regular chaotic behaviour without sinks or sources for subcritical values of the gain–loss parameter. This is an example of what is known in classical dynamical systems as reversible dynamical systems. For large values of the kicking strength a strange attractor is observed that also persists if PT-symmetry is broken. The intensity dynamics of the classical map is investigated, and found to provide the main structure for the Husimi distributions of the subspaces of the quantum system belonging to certain ranges of the imaginary parts of the quasienergies. Classical structures are also identified in the quantum dynamics. Finally, the statistics of the eigenvalues of the quantum system are analysed and it is shown that if most of the eigenvalues are complex (which is the case already for fairly small non-Hermiticity parameters) the nearest-neighbour distances of the (unfolded) quasienergies follow a two-dimensional Posisson distribution when the classical dynamics is regular. In the chaotic regime, on the other hand they are in line with recently identified universal complex level spacing distributions for non-Hermitian systems, with transpose symmetry ÂT = Â. It is demonstrated how breaking this symmetry (by introducing an extra term in the Hamiltonian) recovers the more familiar universality class for non-Hermitian systems given by the complex Ginibre ensemble. Both universality classes display cubic level repulsion. The PT-symmetry of the system does not seem to influence the complex level spacings. Similar behaviour is also observed for the spectrum of a PT-symmetric extension of the triadic Baker map.
Date Issued
2020-10-01
Date Acceptance
2020-08-25
Citation
New Journal of Physics, 2020, 22
ISSN
1367-2630
Publisher
Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft
Journal / Book Title
New Journal of Physics
Volume
22
Copyright Statement
© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Sponsor
The Royal Society
Commission of the European Communities
Identifier
http://arxiv.org/abs/1912.09412v1
Grant Number
UF130339
758453
Subjects
quant-ph
quant-ph
math-ph
math.MP
Notes
18 pages, 14 figures
Publication Status
Published online
Date Publish Online
2020-10-01