与费米气体相互作用的杂质粒子的有效极化子动力学
Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas
AI总结：
本研究针对三维周期方盒中与杂质耦合的均匀理想费米气体，证明大费米动量下其有效动力学由Fröhlich型极化子哈密顿量生成且可用耦合相干态近似，方法适用于多类耦合强度与时间尺度。
摘要：
我们研究了三维周期性边界条件方盒中，与杂质粒子耦合的均匀理想费米气体的量子动力学。对于大费米动量$k_\ ext{F}$，我们证明其有效动力学由Fröhlich型极化子哈密顿量生成，该哈密顿量将杂质粒子与近玻色激发场线性耦合。此外，我们证明有效动力学可由显式耦合相干态近似。我们的方法适用于一系列相互作用耦合，尤其包括1阶相互作用耦合以及$k_\ ext{F}^{-1}$量级的时间尺度。
英文摘要：
We study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a three-dimensional box with periodic boundary condition. For large Fermi momentum $k_\text{F}$, we prove that the effective dynamics is generated by a Fröhlich-type polaron Hamiltonian, which linearly couples the impurity particle to an almost-bosonic excitation field. Moreover, we prove that the effective dynamics can be approximated by an explicit coupled coherent state. Our method is applicable to a range of interaction couplings, in particular including interaction couplings of order 1 and time scales of the order $k_\text{F}^{-1}$.
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