The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier
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| Format: | Preprint |
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2024
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| _version_ | 1866913405116350464 |
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| author | Ragan, Robert J. Sakhel, Asaad R. Mullin, William J. |
| author_facet | Ragan, Robert J. Sakhel, Asaad R. Mullin, William J. |
| contents | The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $δ$-function central barrier. We find solutions that have the symmetry of the non-interacting Hamiltonian as well as asymmetric solutions that bifurcate from the symmetric solutions for attractive interactions and from the antisymmetric solutions for repulsive interactions. We present a variational approximation to the asymmetric state as well as an approximate numerical approach. Stability of the states is briefly considered. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_13833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier Ragan, Robert J. Sakhel, Asaad R. Mullin, William J. Quantum Physics Quantum Gases The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $δ$-function central barrier. We find solutions that have the symmetry of the non-interacting Hamiltonian as well as asymmetric solutions that bifurcate from the symmetric solutions for attractive interactions and from the antisymmetric solutions for repulsive interactions. We present a variational approximation to the asymmetric state as well as an approximate numerical approach. Stability of the states is briefly considered. |
| title | The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2401.13833 |