Non-equilibrium Quantum Simulations using Thimble Methods
Our understanding of time dependent phenomena in particle physics is hampered by our inability to effectively investigate non-equilibrium phenomena, even using computers, due to the ‘Sign Problem’. This problem means that for nonperturbative theories, it is functionally impossible to evaluate Feynma...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2023
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| Online Access: | https://eprints.nottingham.ac.uk/74242/ |
| _version_ | 1848800853662629888 |
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| author | Woodward, Simon |
| author_facet | Woodward, Simon |
| author_sort | Woodward, Simon |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Our understanding of time dependent phenomena in particle physics is hampered by our inability to effectively investigate non-equilibrium phenomena, even using computers, due to the ‘Sign Problem’. This problem means that for nonperturbative theories, it is functionally impossible to evaluate Feynman path integrals to calculate the expectation values of operators. Here I present a possible remedy to this problem in the form of Generalised Thimble Techniques which, at great computational cost, suppress the Sign Problem and allow us to make headway in these investigations.
The formalism for moving these path integrals onto a discrete lattice is discussed, and is followed by an explanation of the mechanics of these Thimble techniques. These techniques are then compared, both in terms of approach and in terms of performance, to the other prominent approach to dealing with the Sign Problem, Langevin Dynamics. The implementation of these techniques is then demonstrated by comparing my results with literature, and how to best compensate for the computational cost is considered.
The discussion then turns to how best to take advantage of the non- perturbative nature of these calculations. The lattice is modified, the characteristic imaginary time extension is removed and replaced with a bespoke density matrix, which is sampled independently of the thimble. This removal of the imaginary time extension opens the door to non-equilibrium density matrices, but initially the focus is on ensuring that these modifications are valid, and reproduction of equilibrium results takes priority.
Unfortunately, the requirement to sample the density matrix independently of the thimble poses new computational problems however. The focus therefore briefly returns to optimisations, this time focusing on physical parameters of the system rather than numerical tricks or approximations. With these optimisations higher dimensional simulations are considered, but are still found to be too intensive for the available hardware. Instead, a second field is introduced, allowing the system to start out of equilibrium in a different way. This second field has a higher mass and occupation number, and two different interactions with a range of coupling strengths are considered. This means ‘particle’ decay can be seen between the two fields.
The technique is shown to be promising, but hampered by its high computational cost. Possible routes to reducing this through both improvements to the algorithm and promising developments in hardware are discussed. |
| first_indexed | 2025-11-14T20:58:10Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-74242 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:58:10Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-742422023-12-12T04:40:08Z https://eprints.nottingham.ac.uk/74242/ Non-equilibrium Quantum Simulations using Thimble Methods Woodward, Simon Our understanding of time dependent phenomena in particle physics is hampered by our inability to effectively investigate non-equilibrium phenomena, even using computers, due to the ‘Sign Problem’. This problem means that for nonperturbative theories, it is functionally impossible to evaluate Feynman path integrals to calculate the expectation values of operators. Here I present a possible remedy to this problem in the form of Generalised Thimble Techniques which, at great computational cost, suppress the Sign Problem and allow us to make headway in these investigations. The formalism for moving these path integrals onto a discrete lattice is discussed, and is followed by an explanation of the mechanics of these Thimble techniques. These techniques are then compared, both in terms of approach and in terms of performance, to the other prominent approach to dealing with the Sign Problem, Langevin Dynamics. The implementation of these techniques is then demonstrated by comparing my results with literature, and how to best compensate for the computational cost is considered. The discussion then turns to how best to take advantage of the non- perturbative nature of these calculations. The lattice is modified, the characteristic imaginary time extension is removed and replaced with a bespoke density matrix, which is sampled independently of the thimble. This removal of the imaginary time extension opens the door to non-equilibrium density matrices, but initially the focus is on ensuring that these modifications are valid, and reproduction of equilibrium results takes priority. Unfortunately, the requirement to sample the density matrix independently of the thimble poses new computational problems however. The focus therefore briefly returns to optimisations, this time focusing on physical parameters of the system rather than numerical tricks or approximations. With these optimisations higher dimensional simulations are considered, but are still found to be too intensive for the available hardware. Instead, a second field is introduced, allowing the system to start out of equilibrium in a different way. This second field has a higher mass and occupation number, and two different interactions with a range of coupling strengths are considered. This means ‘particle’ decay can be seen between the two fields. The technique is shown to be promising, but hampered by its high computational cost. Possible routes to reducing this through both improvements to the algorithm and promising developments in hardware are discussed. 2023-12-12 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/74242/1/Thesis_Corrected.pdf Woodward, Simon (2023) Non-equilibrium Quantum Simulations using Thimble Methods. PhD thesis, University of Nottingham. particle physics non-equilibrium phenomena quantum fields lattice field theory |
| spellingShingle | particle physics non-equilibrium phenomena quantum fields lattice field theory Woodward, Simon Non-equilibrium Quantum Simulations using Thimble Methods |
| title | Non-equilibrium Quantum Simulations using Thimble Methods |
| title_full | Non-equilibrium Quantum Simulations using Thimble Methods |
| title_fullStr | Non-equilibrium Quantum Simulations using Thimble Methods |
| title_full_unstemmed | Non-equilibrium Quantum Simulations using Thimble Methods |
| title_short | Non-equilibrium Quantum Simulations using Thimble Methods |
| title_sort | non-equilibrium quantum simulations using thimble methods |
| topic | particle physics non-equilibrium phenomena quantum fields lattice field theory |
| url | https://eprints.nottingham.ac.uk/74242/ |