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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.04279 |
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| _version_ | 1866918392631394304 |
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| author | Chen, Qian-Can Liu, I-Kang Li, Jheng-Wei Chung, Chia-Min |
| author_facet | Chen, Qian-Can Liu, I-Kang Li, Jheng-Wei Chung, Chia-Min |
| contents | We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics of BECs--including vortex lattice formation and breathing modes--demonstrating superior performance over conventional grid-based methods and stable long-time evolution due to saturating bond dimensions. This establishes QTT as a powerful tool for nonlinear quantum simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics Chen, Qian-Can Liu, I-Kang Li, Jheng-Wei Chung, Chia-Min Quantum Gases Strongly Correlated Electrons We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics of BECs--including vortex lattice formation and breathing modes--demonstrating superior performance over conventional grid-based methods and stable long-time evolution due to saturating bond dimensions. This establishes QTT as a powerful tool for nonlinear quantum simulations. |
| title | Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics |
| topic | Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2507.04279 |