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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2506.20126 |
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| _version_ | 1866913911798759424 |
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| author | Ruby, V. Chithiika Lakshmanan, M. |
| author_facet | Ruby, V. Chithiika Lakshmanan, M. |
| contents | Painlevé's singularity structure analysis, combined with stereographic mapping, has previously been applied to a one-dimensional Heisenberg spin-chain continuum model which identified a Hamiltonian density for the static version of the Landau-Lifshitz equation. In this work, we explore the equivalence of the Hamiltonian density to the nonlinear sigma model. It reveals its non-standard form and can be interpreted as a position-dependent mass Hamiltonian density. We then proceed with the quantization of this Hamiltonian density using the pre-canonical quantization procedure. The resulting Schrödinger-like equation was found to take the form of a confluent Heun equation. By employing the functional Bethe-Ansatz method, we explicitly obtain the ground state and first excited state of the system. This analysis provides a comprehensive quantum description of the system, capturing the probabilistic structure of the field and information about the possible energy states of the spin system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Quantum Approach to the Continuum Heisenberg Spin-Chain Model: Position-Dependent Mass Formalism and Pre-canonical Quantization Ruby, V. Chithiika Lakshmanan, M. Quantum Physics Painlevé's singularity structure analysis, combined with stereographic mapping, has previously been applied to a one-dimensional Heisenberg spin-chain continuum model which identified a Hamiltonian density for the static version of the Landau-Lifshitz equation. In this work, we explore the equivalence of the Hamiltonian density to the nonlinear sigma model. It reveals its non-standard form and can be interpreted as a position-dependent mass Hamiltonian density. We then proceed with the quantization of this Hamiltonian density using the pre-canonical quantization procedure. The resulting Schrödinger-like equation was found to take the form of a confluent Heun equation. By employing the functional Bethe-Ansatz method, we explicitly obtain the ground state and first excited state of the system. This analysis provides a comprehensive quantum description of the system, capturing the probabilistic structure of the field and information about the possible energy states of the spin system. |
| title | A Quantum Approach to the Continuum Heisenberg Spin-Chain Model: Position-Dependent Mass Formalism and Pre-canonical Quantization |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.20126 |