与光子场耦合的量子振子的有效态密度
Effective density of states for a quantum oscillator coupled to a photon field
摘要：
在偶极近似下，给出了简谐束缚粒子与光子场最小耦合的有效配分函数的显式表达式。有效的配分函数被证明是一个积极的Borel措施，有效措施的状态的拉普拉斯变换。后者的绝对连续部分允许解析延拓，其奇点引起共振。我们给出了这些奇点的精确位置，并表明它们是很好地近似的一阶极点的剩余等于相应的本征空间的非耦合量子振荡器的重数。从而得到了带电振子自然线谱的完整解析描述。
英文摘要：
We give an explicit formula for the effective partition function of a harmonically bound particle minimally coupled to a photon field in the dipole approximation. The effective partition function is shown to be the Laplace transform of a positive Borel measure, the effective measure of states. The absolutely continuous part of the latter allows for an analytic continuation, the singularities of which give rise to resonances. We give the precise location of these singularities, and show that they are well approximated by of first order poles with residues equal the multiplicities of the corresponding eigenspaces of the uncoupled quantum oscillator. Thus we obtain a complete analytic description of the natural line spectrum of the charged oscillator.
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