Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator
- URL: http://arxiv.org/abs/2604.22945v1
- Date: Fri, 24 Apr 2026 18:37:30 GMT
- Title: Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator
- Abstract summary: We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU (1,1)$ group.<n>We compute the field quadrature and the survival probability, showing that the Dunkl parameter $$ modulates the fractional revivals.<n>We analyze the quadrature variance to show that the Dunkl deformation generates interference-induced squeezed states around $t approx $.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $μ$ 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 $μ\rightarrow 0$.
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