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arXiv · 2604.22945

Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator

D. Ojeda-Guillén·R. D. Mota·M. Salazar-Ramírez
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Abstract

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 $\mu$ 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 $t \approx \pi$. The standard Kerr medium dynamics are exactly recovered in the limit $\mu \rightarrow 0$.

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D. Ojeda-Guillén, R. D. Mota, M. Salazar-Ramírez. 2026-04-24. Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator. https://doi.org/10.1016/j.aop.2026.170644

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