有限温度下量子声动力学中的红外问题
Infrared problem in quantum acoustodynamics at finite temperature
摘要：
利用线性原子-声子相互作用模型，在弱耦合区研究了非零温度下慢运动原子碰撞弹性膜的声子辅助粘附率.原子-声子耦合中的吸附速率的微扰展开在零温度下是红外发散的，并且有限温度加剧了这个红外问题。然而，在计算中使用的相干态声子的基础上，产生红外有限的结果，即使在有限的温度。与任何有限数量的声子发射的粘附概率被明确地看到是指数小，它消失的膜尺寸的增长，这是以前在零温度下发现的结果;与零温度的情况下，这种指数抑制粘附概率持续甚至与无限数量的软声子的发射。得到了有限温度下软声子发射对吸附速率影响的显式封闭表达式。对于缓慢运动的原子，该模型预测，在非零温度和弱耦合下，粘在大弹性膜上的概率为零。
英文摘要：
The phonon-assisted sticking rate of slow moving atoms impinging on an elastic membrane at nonzero temperature is studied analytically using a model with linear atom-phonon interactions, valid in the weak coupling regime. A perturbative expansion of the adsorption rate in the atom-phonon coupling is infrared divergent at zero temperature, and this infrared problem is exacerbated by finite temperature. The use of a coherent state phonon basis in the calculation, however, yields infrared-finite results even at finite temperature. The sticking probability with the emission of any finite number of phonons is explicitly seen to be exponentially small, and it vanishes as the membrane size grows, a result that was previously found at zero temperature; in contrast to the zero temperature case, this exponential suppression of the sticking probability persists even with the emission of an infinite number of soft phonons. Explicit closed-form expressions are obtained for the effects of soft-phonon emission at finite temperature on the adsorption rate. For slowly moving atoms, the model predicts that there is zero probability of sticking to a large elastic membrane at nonzero temperature and weak coupling.
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