周期碰撞量子系统Floquet算符的连续谱分量
On the continuous spectral component of the Floquet operator for a periodically kicked quantum system
摘要：
通过一个简单的概括，我们扩展了工作的Combescure从秩1到秩N扰动。建立了Floquet算子为纯点的条件，并与Combescure算子进行了比较。结果与McCaw的结果一致。这里的方法是该工作的替代方案。我们证明了，如果放松Floquet算子为纯点的条件，那么在Delta-kicked谐振子的情况下，Floquet算子谱存在一个奇连续分量.我们还提供了一个深入的讨论，在Combescure的情况下，未扰动的哈密顿量是更一般的猜想。我们链接的物理猜想直接到数论猜想的维诺格拉多夫和表明，解决维诺格拉多夫的猜想解决了物理猜想。将结果推广到秩N的情形。讨论了我们的工作与布尔歇关于物理学猜想的工作之间的关系。
英文摘要：
By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.
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