原子-场系统的比较量子和半经典分析I：态密度和激发态量子相变
Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
摘要：
我们研究了不可积的Dicke模型及其可积的近似Tavis-Cummings模型作为耦合常数和激发能的函数。激发态的量子相变（ESQPT）被发现在半经典极限分析状态的密度，并将其与数值计算结果的量子情况下，在大希尔伯特空间，利用最近发展的有效方法的优势。两个不同的ESQPT被确定在两个模型中，这是信号作为奇异的半经典态密度，一个{ \em静态} ESQPT发生任何耦合，而动态ESQPT只观察到在超辐射相。讨论并确定了哈密顿半经典流的不稳定不动点在ESQPT发生中的作用。数值证据表明，半经典的结果很好地描述了量子能谱的任何耦合在这两个模型中的趋势。因此，半经典态密度可以用来研究谱中涨落的统计特性，这一研究在一篇配套论文中提出。
英文摘要：
We study the non-integrable Dicke model, and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semi-classical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semi-classical density of states, one {\em static} ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semi-classical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semi-classical result describes very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore the semi-classical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.
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