Chaos and Scrambling in Quantum Small Worlds
| dc.contributor.advisor | Murugan, Jeffrey | |
| dc.contributor.advisor | Shock, Jonathan | |
| dc.contributor.author | Hartmann, Jean-Gabriel Keiser | |
| dc.date.accessioned | 2020-09-15T09:28:07Z | |
| dc.date.available | 2020-09-15T09:28:07Z | |
| dc.date.issued | 2020 | |
| dc.date.updated | 2020-09-14T22:40:08Z | |
| dc.description.abstract | In this thesis, we introduce a novel class of many-body quantum system, which we term ‘quantum small worlds'. These are strongly-interacting systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. They are systems of quantum spin particles in which the network topology is given by the Watts-Strogatz model of network theory. As such, they furnish a novel laboratory for studying quantum systems transitioning between integrable and non-integrable behaviour. Our motivation is to understand how the dynamics of the system are affected by this transition, particularly with regards to the ability of the system to scramble (quantum) information, and potential emergence of chaotic behaviour. Our work begins with a review of the relevant literature regarding algebraic graph theory and quantum chaos. Next, we introduce the model by starting from a well understood integrable system, a spin- 1 2 Heisenberg, or Ising, chain. We then inject a small number of long-range interactions and study its ability to scramble quantum information using two primary devices: the out-of-time-order correlator (OTOC) and the spectral form factor (SFF). We find that the system shows increasingly rapid scrambling as its interactions become progressively more random, with no evidence of quantum chaos as diagnosed by either of these devices. | |
| dc.identifier.apacitation | Hartmann, J. K. (2020). <i>Chaos and Scrambling in Quantum Small Worlds</i>. (). ,Faculty of Science ,Department of Maths and Applied Maths. Retrieved from http://hdl.handle.net/11427/32266 | en_ZA |
| dc.identifier.chicagocitation | Hartmann, Jean-Gabriel Keiser. <i>"Chaos and Scrambling in Quantum Small Worlds."</i> ., ,Faculty of Science ,Department of Maths and Applied Maths, 2020. http://hdl.handle.net/11427/32266 | en_ZA |
| dc.identifier.citation | Hartmann, J.K. 2020. Chaos and Scrambling in Quantum Small Worlds. . ,Faculty of Science ,Department of Maths and Applied Maths. http://hdl.handle.net/11427/32266 | en_ZA |
| dc.identifier.ris | TY - Master Thesis AU - Hartmann, Jean-Gabriel Keiser AB - In this thesis, we introduce a novel class of many-body quantum system, which we term ‘quantum small worlds'. These are strongly-interacting systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. They are systems of quantum spin particles in which the network topology is given by the Watts-Strogatz model of network theory. As such, they furnish a novel laboratory for studying quantum systems transitioning between integrable and non-integrable behaviour. Our motivation is to understand how the dynamics of the system are affected by this transition, particularly with regards to the ability of the system to scramble (quantum) information, and potential emergence of chaotic behaviour. Our work begins with a review of the relevant literature regarding algebraic graph theory and quantum chaos. Next, we introduce the model by starting from a well understood integrable system, a spin- 1 2 Heisenberg, or Ising, chain. We then inject a small number of long-range interactions and study its ability to scramble quantum information using two primary devices: the out-of-time-order correlator (OTOC) and the spectral form factor (SFF). We find that the system shows increasingly rapid scrambling as its interactions become progressively more random, with no evidence of quantum chaos as diagnosed by either of these devices. DA - 2020_ DB - OpenUCT DP - University of Cape Town KW - Mathematics and Applied Mathematics LK - https://open.uct.ac.za PY - 2020 T1 - Chaos and Scrambling in Quantum Small Worlds TI - Chaos and Scrambling in Quantum Small Worlds UR - http://hdl.handle.net/11427/32266 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/32266 | |
| dc.identifier.vancouvercitation | Hartmann JK. Chaos and Scrambling in Quantum Small Worlds. []. ,Faculty of Science ,Department of Maths and Applied Maths, 2020 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/32266 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Maths and Applied Maths | |
| dc.publisher.faculty | Faculty of Science | |
| dc.subject | Mathematics and Applied Mathematics | |
| dc.title | Chaos and Scrambling in Quantum Small Worlds | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MSc |