Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915956071071744 |
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| author | Ojeda-Guillén, D. Mota, R. D. Salazar-Ramírez, M. |
| author_facet | Ojeda-Guillén, D. Mota, R. D. Salazar-Ramírez, M. |
| contents | We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU(1,1)$ group. In order to obtain the exact energy spectrum of this problem, we write its Hamiltonian in terms of the Dunkl creation and annihilation operators, which close the $su(1,1)$ Lie algebra. This allows us to exactly solve this Hamiltonian and obtain its parity-dependent energy spectrum. Then, we investigate the quantum dynamics of the system, particularly the collapse and revival phenomena, by using an initial state given by a superposition of even and odd Dunkl coherent states. We compute the field quadrature and the survival probability, showing that the Dunkl parameter $μ$ modulates the fractional revivals and produces perfect state reconstructions at half-periods for specific deformation values. We analyze the quadrature variance to show that the Dunkl deformation generates interference-induced squeezed states around $t \approx π$. The standard Kerr medium dynamics are exactly recovered in the limit $μ\rightarrow 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22945 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator Ojeda-Guillén, D. Mota, R. D. Salazar-Ramírez, M. Quantum Physics Mathematical Physics We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU(1,1)$ group. In order to obtain the exact energy spectrum of this problem, we write its Hamiltonian in terms of the Dunkl creation and annihilation operators, which close the $su(1,1)$ Lie algebra. This allows us to exactly solve this Hamiltonian and obtain its parity-dependent energy spectrum. Then, we investigate the quantum dynamics of the system, particularly the collapse and revival phenomena, by using an initial state given by a superposition of even and odd Dunkl coherent states. We compute the field quadrature and the survival probability, showing that the Dunkl parameter $μ$ modulates the fractional revivals and produces perfect state reconstructions at half-periods for specific deformation values. We analyze the quadrature variance to show that the Dunkl deformation generates interference-induced squeezed states around $t \approx π$. The standard Kerr medium dynamics are exactly recovered in the limit $μ\rightarrow 0$. |
| title | Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2604.22945 |