论文标题
语音子红移和哈勃摩擦不断扩展
Phonon redshift and Hubble friction in an expanding BEC
论文作者
论文摘要
我们重新审查了膨胀的环形玻色网凝结物的理论分析。从动作到尺寸正交到声子的旅行方向开始，我们得出了一个有效的方程，适用于方差方程。该波方程表明，膨胀以由有效方位角声速度确定的速率进行红移，并以$ \ dot {\ cal V}/{\ cal V} $给出的速率抑制声子的振幅，其中$ \ cal {v} $是背景冷凝水的体积。这种行为类似于扩展宇宙中量子场的红变和“哈勃摩擦”，并且鉴于用环电位形状确定半径的尺度，与最近的实验和理论结果一致。此处使用的基于动作的尺寸还原方法应适用于各种设置，并且非常适合系统的扰动扩展。
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.
