Oruç, Tunay (2024) Integrable Open Quantum Systems. Bachelor's Thesis, Physics.
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Abstract
Over the past century, Open Quantum Systems –quantum systems that interact with their environment— and Quantum Integrable Systems –quantum systems that are exactly solvable— were viewed as separate fields. However, in recent years, various Integrable Open Quantum Systems have been classified and gained considerable popularity. The approach in classifying such systems is the Boost Automorphism Method -- a bottom-up method in which the corresponding $R$-matrix is constructed from an Hamiltonian ansatz through a boost operator. The resultant $R$-matrix solves the Yang-Baxter equation, ensuring the integrability of the model. This thesis aims to review the classification of Integrable Open Quantum Systems and examine a concrete example -- referred to as Model A1. To this end, this thesis first presents the mathematical formulation of Open Quantum Systems, followed by its dynamics -- the derivation of the Lindblad equation. Subsequently, integrability is introduced through the representative example of the Heisenberg Spin Chain, along with the $R$-matrix and the Yang-Baxter Equation. Moreover, the Boost Automorphism Method is explained in detail with a concrete example. Ultimately, all notions are connected and the classification of Integrable Open Quantum Systems is concluded.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Gorbe, T.F. and Mazumdar, A. |
| Degree programme: | Physics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 13 Dec 2024 09:41 |
| Last Modified: | 13 Dec 2024 09:41 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33310 |
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