Dicke模型的近似可积性
Approximated integrability of the Dicke model
摘要：
在基态以上的一个很宽的区域内，并为广泛的外部参数的值的范围内，一个非常近似的Dicke模型的运动的第二积分。这第二个积分，从玻恩奥本海默近似，分类的整个正规部分的频谱的频带标记其相应的本征值。从这种近似得到的结果进行了比较，在超辐射相的有限系统的精确数值对角化，获得了显着的协议。我们的方法在参数空间，其中包括共振的情况下，有效性的区域被揭开。有效性的能量范围从基态到一定的上能量，其中混沌集，并远远超出了最小能量配置周围的简谐近似的适用范围。能量有效性上限随着耦合常数和能级分裂与场频率之比的增大而增大。这些结果表明，Dicke模型的行为像一个两自由度的可积模型的能量和值的外部参数的范围很宽。
英文摘要：
A very approximate second integral of motion of the Dicke model is identified within a broad region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born Oppenheimer approximation, classifies the whole regular part of the spectrum in bands labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree of freedom integrable model for a wide range of energies and values of the external parameters.
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