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Chaos and Scrambling in Quantum Small Worlds
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...
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| Format: | Thesis |
| Language: | English |
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Department of Maths and Applied Maths
2020
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| _version_ | 1867614269160292352 |
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| access_status_str | Open Access |
| author | Hartmann, Jean-Gabriel Keiser |
| author2 | Murugan, Jeffrey |
| author_browse | Hartmann, Jean-Gabriel Keiser Murugan, Jeffrey |
| author_facet | Murugan, Jeffrey Hartmann, Jean-Gabriel Keiser |
| author_sort | Hartmann, Jean-Gabriel Keiser |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32266 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:49:21.452Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | Department of Maths and Applied Maths |
| publisherStr | Department of Maths and Applied Maths |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/32266 Chaos and Scrambling in Quantum Small Worlds Hartmann, Jean-Gabriel Keiser Murugan, Jeffrey Shock, Jonathan Mathematics and Applied Mathematics 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. 2020-09-15T09:28:07Z 2020-09-15T09:28:07Z 2020 2020-09-14T22:40:08Z Master Thesis Masters MSc http://hdl.handle.net/11427/32266 eng application/pdf Department of Maths and Applied Maths Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Hartmann, Jean-Gabriel Keiser Chaos and Scrambling in Quantum Small Worlds |
| thesis_degree_str | Master's |
| title | Chaos and Scrambling in Quantum Small Worlds |
| title_full | Chaos and Scrambling in Quantum Small Worlds |
| title_fullStr | Chaos and Scrambling in Quantum Small Worlds |
| title_full_unstemmed | Chaos and Scrambling in Quantum Small Worlds |
| title_short | Chaos and Scrambling in Quantum Small Worlds |
| title_sort | chaos and scrambling in quantum small worlds |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/32266 |
| work_keys_str_mv | AT hartmannjeangabrielkeiser chaosandscramblinginquantumsmallworlds |