示踪粒子与玻色-爱因斯坦凝聚体激发态相互作用的动力学
Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensate
摘要：
本文研究了环面上大量相互作用的$N$玻色子与示踪粒子（另一种粒子）耦合的量子动力学。我们假设在初始状态下，玻色子基本上形成一个均匀的玻色-爱因斯坦凝聚体，并带有一些激发。通过适当的平均场尺度的相互作用，我们证明了有效的动力学$N\to \infty$产生的Bogoliubov-Fröhlich哈密顿量，它耦合的示踪粒子线性的激发场。
英文摘要：
We consider the quantum dynamics of a large number $N$ of interacting bosons coupled a tracer particle, i.e. a particle of another kind, on a torus. We assume that in the initial state the bosons essentially form a homogeneous Bose-Einstein condensate, with some excitations. With an appropriate mean-field scaling of the interactions, we prove that the effective dynamics for $N\to \infty$ is generated by the Bogoliubov-Fröhlich Hamiltonian, which couples the tracer particle linearly to the excitation field.
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