Kavanagh, Kevin
(2022)
Topological Aspects of 1-Dimensional
Closed & Open Quantum Systems.
PhD thesis, National University of Ireland Maynooth.
Abstract
We consider the p-wave superconductor in one spatial dimension from two perspectives.
Firstly as a closed system and secondly as an open system.
As a closed system, we analyse the p-wave superconductor as a candidate platform
which can host Majorana bound states. In particular, we consider how interaction
driven errors could spoil the encoding of protected qubit states constructed from
these bound states. We present a generic analysis of how the property of topological
quantum order (TQO) suppresses an interaction driven dephasing process.
We use this to quantify the extent of correlation between spectral densities from
different topological sectors. Our key result, verified numerically for the p-wave superconductor,
is that despite mismatched bulk spectra the TQO property ensures
that interaction driven phase errors are suppressed up to a time which scales with
system length.
As an open system, we bring the model into contact with various environments.
We do so to understand the interplay of quantum and classical transport phenomena.
Our key result in this case is that there is, in general, a strong dependence on
the superconductor pairing and the boundary dissipation rates in the final nonequilibrium
steady states. Further, we demonstrate that under weak dissipation
topological properties of the closed system manifest themselves in a key aspect of
the open quantum system dynamics, the Liouvillian gap. We find that this indicator
of relaxation time retains information of these properties robustly for a number of
dissipative processes.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
Topological Aspects; 1-Dimensional
Closed & Open Quantum Systems; |
| Academic Unit: |
Faculty of Science and Engineering > Theoretical Physics |
| Item ID: |
17088 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
03 Apr 2023 13:55 |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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