Dunkl非谐振子中的量子动力学与坍缩-复兴现象
Quantum Dynamics and Collapse-and-Revival Phenomena in the Dunkl Anharmonic Oscillator
AI总结：
本文通过SU(1,1)群的代数方法研究Dunkl非谐振子，推导出其能量谱并分析系统动力学中的坍缩与复兴现象，揭示Dunkl参数对分数复兴和完美态重构的影响。
摘要：
我们从SU(1,1)群的代数方法出发，研究Dunkl非谐振子（Kerr介质）哈密顿量。为获得该问题的精确能谱，我们将其哈密顿量用Dunkl产生和湮灭算符表示，这些算符闭合su(1,1)李代数。这使得我们可以精确求解该哈密顿量并获得与其奇偶性相关的能谱。然后，我们通过初始态为偶奇Dunkl相干态的叠加，研究系统的量子动力学，特别是坍缩与复兴现象。我们计算了场二次量和存活概率，显示Dunkl参数μ调节分数复兴并产生特定变形值下的完美态重构。我们分析了二次量方差，表明Dunkl变形在t≈π附近生成干涉诱导的压缩态。标准Kerr介质动力学在μ→0极限下被精确恢复。
英文摘要：
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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