arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1611.09445cond-mat.mes-hallcond-mat.quant-gasquant-ph
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量子声学中的红外问题

Infrared Problem in Quantum Acoustodynamics

Dennis P. Clougherty, Sanghita Sengupta

摘要:

量子电动力学(QED)提供了一个高度精确的描述,涉及原子与光的相互作用的现象。我们认为,描述冷原子与振动膜相互作用的量子理论--量子声动力学(QAD)--与QED有许多共同的问题和特征。具体来说,原子在振动膜上的吸附可以被看作是QED辐射电子捕获的对应物。在原子-声子耦合的最低阶的吸附率的计算是有限的,然而,高阶的贡献遭受红外问题模仿的情况下,在QED的辐射捕获。作为模型中无质量粒子(QAD中膜的弯曲声子和QED中的光子)的结果,吸附速率的微扰系列中的项发散。我们对待这个红外问题QAD明确获得有限的结果,通过正则化与低频截止对应的膜的大小的倒数。使用软声子的最终状态的相干态的基础上,我们然后总结的主要贡献,推导出一个新的公式的多声子吸附率的原子上的膜,给出的结果是有限的,非微扰的原子-声子耦合,并与KLN定理一致。对于微膜,我们预测随着膜尺寸的增加,低能量的吸附率降低。我们讨论了这一点的相关性的原子氢的冷气体的吸附在悬浮的石墨烯。

英文摘要:

Quantum electrodynamics (QED) provides a highly accurate description of phenomena involving the interaction of atoms with light. We argue that the quantum theory describing the interaction of cold atoms with a vibrating membrane--quantum acoustodynamics (QAD)--shares many issues and features with QED. Specifically, the adsorption of an atom on a vibrating membrane can be viewed as the counterpart to QED radiative electron capture. A calculation of the adsorption rate to lowest-order in the atom-phonon coupling is finite; however, higher-order contributions suffer from an infrared problem mimicking the case of radiative capture in QED. Terms in the perturbation series for the adsorption rate diverge as a result of massless particles in the model (flexural phonons of the membrane in QAD and photons in QED). We treat this infrared problem in QAD explicitly to obtain finite results by regularizing with a low-frequency cutoff that corresponds to the inverse size of the membrane. Using a coherent state basis for the soft phonon final state, we then sum the dominant contributions to derive a new formula for the multiphonon adsorption rate of atoms on the membrane that gives results that are finite, nonperturbative in the atom-phonon coupling, and consistent with the KLN theorem. For micromembranes, we predict a reduction with increasing membrane size for the low-energy adsorption rate. We discuss the relevance of this to the adsorption of a cold gas of atomic hydrogen on suspended graphene.

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