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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/2509.01995 |
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| _version_ | 1866908815073476608 |
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| author | Camus-Sais, Marc Rojo-Francàs, Abel Astrakharchik, Grigori E. Juliá-Díaz, Bruno |
| author_facet | Camus-Sais, Marc Rojo-Francàs, Abel Astrakharchik, Grigori E. Juliá-Díaz, Bruno |
| contents | We propose a discrete-space representation of a one-dimensional zero-range odd-parity pseudopotential. The proposed representation is validated by applying it to the analytically solvable case of two fermions in a harmonic trap and successfully recovering the exact energy spectrum and eigenfunctions. Furthermore, we use the square-well and modified Pöschl--Teller potentials as finite-range representations of the odd-parity interaction and study their convergence to the contact interaction when the range tends to zero. Finally, we perform natural orbital analysis and compute the eigenvalues of the one-body density matrix for different particle numbers, examining their dependence on the one-dimensional scattering length and identifying distinct physical regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coordinate space representation of a one-dimensional odd-parity pseudopotential Camus-Sais, Marc Rojo-Francàs, Abel Astrakharchik, Grigori E. Juliá-Díaz, Bruno Quantum Gases We propose a discrete-space representation of a one-dimensional zero-range odd-parity pseudopotential. The proposed representation is validated by applying it to the analytically solvable case of two fermions in a harmonic trap and successfully recovering the exact energy spectrum and eigenfunctions. Furthermore, we use the square-well and modified Pöschl--Teller potentials as finite-range representations of the odd-parity interaction and study their convergence to the contact interaction when the range tends to zero. Finally, we perform natural orbital analysis and compute the eigenvalues of the one-body density matrix for different particle numbers, examining their dependence on the one-dimensional scattering length and identifying distinct physical regimes. |
| title | Coordinate space representation of a one-dimensional odd-parity pseudopotential |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2509.01995 |