广义Jahn-Teller格子模型中的量子相交叉与混沌
Quantum phase crossover and chaos in generalized Jahn-Teller lattice model
摘要：
有限晶格上的广义多自旋Jahn-Teller模型或形式上等价的Dicke模型扩展到两个不同频率的长波长相干玻色子，表现出极化子修改的“准正常”和压缩的“辐射”域之间的交叉。我们研究了两种干扰涨落对玻色子复谱的相位交叉和统计特性的影响：（1）电子子系统中的涨落--有限尺寸的量子涨落--是辐射域相干性退相和正常域激发态适度占据的原因。在准经典极限下，辐射相意味着相干声超辐射相的存在。(ii)具有强能级排斥的激发玻色子能级子系统中的能级间距涨落。相关的概率分布被证明是非普遍传播之间的限制普遍维格纳-戴森和泊松分布。我们证明了玻色子频率的差异是达到Wigner-Dyson分布最随机极限的原因。瞬子晶格作为最混沌的辐射域中的隧穿事件序列，表现出最大数量的能级回避（排斥）。这种分布的非普适性是由玻色子关联引起的，玻色子关联与能级排斥相竞争。
英文摘要：
The generalized multispin Jahn-Teller model on a finite lattice or formally equivalent Dicke model extended to two long-wavelength coherent bosons of different frequencies is shown to exhibit a crossover between the polaron-modified "quasi-normal" and the squeezed "radiation" domains. We investigate effects of two kinds of interfering fluctuations on the phase crossover and on statistical characteristics of boson complex spectra: (i) Fluctuations in the electron subsystem- finite-size quantum fluctuations- are responsible for the dephasing of the coherence in the radiation domain and for the moderate occupation of the excited states in the normal domain. In the quasiclassical limit, radiation phase implies existence of a coherent acoustic super-radiant phase. (ii) Level-spacing fluctuations in excited boson level subsystem with strong level repulsions. Related probability distributions are shown to be non-universally spread between the limiting universal Wigner-Dyson and Poisson distributions. We proved that the difference in boson frequencies is responsible for reaching the most stochastic limit of the Wigner-Dyson distribution. Instanton lattice as a sequence of tunneling events in the most chaotic radiation domain exhibits maximal number of level-avoidings (repulsions). The non-universality of the distributions is caused by boson correlations which compete the level repulsions.
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