高密度极限下示踪粒子与费米气体耦合的自由时间演化
Free time evolution of a tracer particle coupled to a Fermi gas in the high-density limit
摘要：
研究了二维空间中粒子与稠密均匀理想费米气体的耦合动力学。我们分析耦合参数g=1的模型（即，不是在弱耦合制度），并证明接近的时间演化的有效动力学的大密度的气体和长时间尺度的一些权力的密度的顺序。有效的动力学产生的自由哈密顿与一个大的，但恒定的能量转移，这是在领先的顺序由空间均匀的平均场势的气体粒子。在这里，平均场近似原来是准确的，虽然波动的潜力周围的平均值可以是任意大的。我们的结果与稠密玻色子气体相反，在稠密玻色子气体中，示踪粒子的自由运动在很短的时间尺度上就已经受到干扰。证明是基于使用强相位抵消的平均场时间演化的微观动力学的偏差。
英文摘要：
The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g=1 (i.e., not in the weak coupling regime), and prove closeness of the time evolution to an effective dynamics for large densities of the gas and for long time scales of the order of some power of the density. The effective dynamics is generated by the free Hamiltonian with a large but constant energy shift which is given at leading order by the spatially homogeneous mean field potential of the gas particles. Here, the mean field approximation turns out to be accurate although the fluctuations of the potential around its mean value can be arbitrarily large. Our result is in contrast to a dense bosonic gas in which the free motion of a tracer particle would be disturbed already on a very short time scale. The proof is based on the use of strong phase cancellations in the deviations of the microscopic dynamics from the mean field time evolution.
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