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Chaotic behavior and energy polarisation in flatband lattice models
Flatbands (FBs) in lattice systems correspond to dispersionless energy bands cre- ated through what is called destructive interference, a phenomenon caused by the existence of lattice symmetries, resulting in compactly localised wave functions to just a few lattice sites. The existence of FBs in mat...
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| Language: | English |
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Department of Mathematics and Applied Mathematics
2024
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| _version_ | 1867614511724232704 |
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| access_status_str | Open Access |
| author | Cheong, Su Ho |
| author2 | Skokos, Charalampos |
| author_browse | Cheong, Su Ho Skokos, Charalampos |
| author_facet | Skokos, Charalampos Cheong, Su Ho |
| author_sort | Cheong, Su Ho |
| collection | Thesis |
| description | Flatbands (FBs) in lattice systems correspond to dispersionless energy bands cre- ated through what is called destructive interference, a phenomenon caused by the existence of lattice symmetries, resulting in compactly localised wave functions to just a few lattice sites. The existence of FBs in materials entails high sensitivity to the initial conditions of the system, especially with regard to disorder and nonlinear- ity. In this study, we numerically investigate the wave packet dynamics and chaotic behaviour of a simple tight-binding system exhibiting FBs, the so-called stub lattice model. Initially we show the existence of a FB and of two dispersive frequency bands for this model and identify three different dynamical regimes, namely the weak chaos, strong chaos, and self trapping regimes. Using symplectic integration techniques, we evolve in time, t, initially localised wave packets for these regimes and quantify their spreading through the computation of the wave packets second moment, m2, while the extent of localisation is characterised using the wave packets participation number. We show that, for both the weak and strong chaos regimes, the spreading of wave packets, which is characterised by a power law increases of m2 (respectively ∝ t0.33 and ∝ t0.5), is a chaotic process whose maximum Lyapunov exponent respectively decreases ∝ t−0.25 and ∝ t−0.3. By decreasing the system's disorder strength we alter the width of the bandgap, something which does not ap- pear to affect the spreading dynamics in the weak chaos regime, while our results do not lead to clear conclusions in the case of strong chaos. Furthermore, we find that particular disorder configurations which preserve the FB do not alter the wave packet spreading dynamics for the weak chaos regime. Finally, we observe that the wave packets norm distributions at the subsites of the stub lattice unit cells reach equilibrium if the evolution time is sufficiently long |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/39314 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:53:12.779Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/39314 Chaotic behavior and energy polarisation in flatband lattice models Cheong, Su Ho Skokos, Charalampos Mathematics Flatbands (FBs) in lattice systems correspond to dispersionless energy bands cre- ated through what is called destructive interference, a phenomenon caused by the existence of lattice symmetries, resulting in compactly localised wave functions to just a few lattice sites. The existence of FBs in materials entails high sensitivity to the initial conditions of the system, especially with regard to disorder and nonlinear- ity. In this study, we numerically investigate the wave packet dynamics and chaotic behaviour of a simple tight-binding system exhibiting FBs, the so-called stub lattice model. Initially we show the existence of a FB and of two dispersive frequency bands for this model and identify three different dynamical regimes, namely the weak chaos, strong chaos, and self trapping regimes. Using symplectic integration techniques, we evolve in time, t, initially localised wave packets for these regimes and quantify their spreading through the computation of the wave packets second moment, m2, while the extent of localisation is characterised using the wave packets participation number. We show that, for both the weak and strong chaos regimes, the spreading of wave packets, which is characterised by a power law increases of m2 (respectively ∝ t0.33 and ∝ t0.5), is a chaotic process whose maximum Lyapunov exponent respectively decreases ∝ t−0.25 and ∝ t−0.3. By decreasing the system's disorder strength we alter the width of the bandgap, something which does not ap- pear to affect the spreading dynamics in the weak chaos regime, while our results do not lead to clear conclusions in the case of strong chaos. Furthermore, we find that particular disorder configurations which preserve the FB do not alter the wave packet spreading dynamics for the weak chaos regime. Finally, we observe that the wave packets norm distributions at the subsites of the stub lattice unit cells reach equilibrium if the evolution time is sufficiently long 2024-04-04T11:25:20Z 2024-04-04T11:25:20Z 2023 2024-04-04T11:10:51Z Thesis / Dissertation Masters MSc http://hdl.handle.net/11427/39314 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics Cheong, Su Ho Chaotic behavior and energy polarisation in flatband lattice models |
| thesis_degree_str | Master's |
| title | Chaotic behavior and energy polarisation in flatband lattice models |
| title_full | Chaotic behavior and energy polarisation in flatband lattice models |
| title_fullStr | Chaotic behavior and energy polarisation in flatband lattice models |
| title_full_unstemmed | Chaotic behavior and energy polarisation in flatband lattice models |
| title_short | Chaotic behavior and energy polarisation in flatband lattice models |
| title_sort | chaotic behavior and energy polarisation in flatband lattice models |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/39314 |
| work_keys_str_mv | AT cheongsuho chaoticbehaviorandenergypolarisationinflatbandlatticemodels |