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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.15326 |
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| _version_ | 1866916464040083456 |
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| author | Lan, Chen Li, Wei Geng, Huifang |
| author_facet | Lan, Chen Li, Wei Geng, Huifang |
| contents | The spectral collocation method (SCM) exhibits a clear superiority in solving ordinary and partial differential equations compared to conventional techniques, such as finite difference and finite element methods. This makes SCM a powerful tool for addressing the Schrödinger-like equations with boundary conditions in physics. However, the Chebyshev differential matrix (CDM), commonly used in SCM to replace the differential operator, is not Hermitian but pseudo-Hermitian. This non-Hermiticity subtly affects the pseudospectra and leads to a loss of completeness in the eigenstates. Consequently, several issues arise with these eigenstates. In this paper, we revisit the non-Hermitian Liouville quantum mechanics by emphasizing the pseudo-Hermiticity of the CDM and explore its expanded models. Furthermore, we demonstrate that the spectral instability can be influenced by the compactification parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics Lan, Chen Li, Wei Geng, Huifang Quantum Physics General Relativity and Quantum Cosmology The spectral collocation method (SCM) exhibits a clear superiority in solving ordinary and partial differential equations compared to conventional techniques, such as finite difference and finite element methods. This makes SCM a powerful tool for addressing the Schrödinger-like equations with boundary conditions in physics. However, the Chebyshev differential matrix (CDM), commonly used in SCM to replace the differential operator, is not Hermitian but pseudo-Hermitian. This non-Hermiticity subtly affects the pseudospectra and leads to a loss of completeness in the eigenstates. Consequently, several issues arise with these eigenstates. In this paper, we revisit the non-Hermitian Liouville quantum mechanics by emphasizing the pseudo-Hermiticity of the CDM and explore its expanded models. Furthermore, we demonstrate that the spectral instability can be influenced by the compactification parameter. |
| title | Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics |
| topic | Quantum Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.15326 |