Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917663182159872 |
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| author | Fujii, Keisuke Görlitz, Sarah L. Liebster, Nikolas Sparn, Marius Kath, Elinor Strobel, Helmut Oberthaler, Markus K. Enss, Tilman |
| author_facet | Fujii, Keisuke Görlitz, Sarah L. Liebster, Nikolas Sparn, Marius Kath, Elinor Strobel, Helmut Oberthaler, Markus K. Enss, Tilman |
| contents | We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by periodic driving of the interatomic interaction. We show that this modulation generically leads to a stable square grid density pattern, due to nonlinear effects beyond the initial Faraday instability. We take the amplitudes of two waves parametrizing the two-dimensional density pattern as order parameters in pattern formation. For these amplitudes, we derive a set of coupled time evolution equations from the Gross--Pitaevskii (GP) equation with a time-periodic interaction. We identify the fixed points of the time evolution and show by stability analysis that the inhomogeneous density exhibits a square grid pattern, which can be understood as a manifestation of a stable fixed point. Our stability analysis establishes the pattern in BECs as a nonequilibrium steady state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_03829 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates Fujii, Keisuke Görlitz, Sarah L. Liebster, Nikolas Sparn, Marius Kath, Elinor Strobel, Helmut Oberthaler, Markus K. Enss, Tilman Quantum Gases Statistical Mechanics Pattern Formation and Solitons We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by periodic driving of the interatomic interaction. We show that this modulation generically leads to a stable square grid density pattern, due to nonlinear effects beyond the initial Faraday instability. We take the amplitudes of two waves parametrizing the two-dimensional density pattern as order parameters in pattern formation. For these amplitudes, we derive a set of coupled time evolution equations from the Gross--Pitaevskii (GP) equation with a time-periodic interaction. We identify the fixed points of the time evolution and show by stability analysis that the inhomogeneous density exhibits a square grid pattern, which can be understood as a manifestation of a stable fixed point. Our stability analysis establishes the pattern in BECs as a nonequilibrium steady state. |
| title | Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates |
| topic | Quantum Gases Statistical Mechanics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2309.03829 |