膨胀BEC中的声子红移和哈勃摩擦
Phonon redshift and Hubble friction in an expanding BEC
摘要：
我们重新讨论了膨胀环形玻色-爱因斯坦凝聚体的理论分析。从声子的作用量出发，在与声子传播方向正交的维度上积分，导出了一个有效的一维方位传播声子的波动方程。该波动方程表明，膨胀使声子频率以由有效方位角声速确定的速率红移，并以由$\dot{\cal V}/{\cal V}$给出的速率阻尼声子的振幅，其中$\cal{V}$是背景凝聚体的体积。这种行为类似于膨胀宇宙中量子场的红移和“哈勃摩擦”，并且，给定由环势形状决定的半径的标度，与最近的实验和理论结果一致。这里使用的基于动作的降维方法应该适用于各种设置，并且非常适合于系统扰动展开。
英文摘要：
We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.
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