可压缩平面量子流体中涡旋与稀疏脉冲的速度关联
Velocity correlations of vortices and rarefaction pulses in compressible planar quantum fluids
AI总结：
本文提出一种定量解析框架计算可压缩量子流体中涡旋与稀疏脉冲的两点速度关联，通过新拟设与渐近分析导出闭式表达式，并与数值模拟结果高度吻合，为表征涡旋和孤子奠定基础。
摘要：
我们提出了一种用于计算可压缩量子流体中两点速度关联的定量解析框架，重点关注两类关键的超流体激发：涡旋与稀疏脉冲。我们采用了两种互补的方法。首先，我们为平面量子流体中的涡旋核引入了一种新的拟设，以增强解析可积性。该拟设为一般涡旋分布的功率谱和速度关联给出了闭式表达式。利用该拟设，我们识别了分别对应于涡旋偶极子和涡旋对的短程和长程速度关联的显著特征。其次，我们分析了 Jones-Roberts 孤子的快速稀疏脉冲区域。通过应用渐近高速波函数，我们导出了速度功率谱和关联函数的解析表达式，捕捉了孤子的特征长度尺度。我们针对均匀系统的解析结果，通过与大型陷俘系统的数值处理进行对比，发现两者存在密切的定量一致性。我们的研究结果为光量子流体中的 Jones-Roberts 孤子速度关联提供了首次解析处理 [M. Baker-Rasooli et al., Physical Review Letters, 134, 233401 (2025)]，并为表征可压缩量子流体中的涡旋和孤子奠定了基础。
英文摘要：
We present a quantitative analytical framework for calculating two-point velocity correlations in compressible quantum fluids, focusing on two key classes of superfluid excitations: vortices and rarefaction pulses. We employ two complementary approaches. First, we introduce a new ansatz for vortex cores in planar quantum fluids that enhances analytic integrability. This ansatz yields closed-form expressions for power spectra and velocity correlations for general vortex distributions. Using it, we identify distinct signatures of short- and long-range velocity correlations corresponding to vortex dipoles and vortex pairs, respectively. Second, we analyze the fast rarefaction pulse regime of the Jones-Roberts soliton. By applying the asymptotic high-velocity wavefunction, we derive analytic expressions for the velocity power spectrum and correlation function, capturing the soliton characteristic length scale. We validate our analytical results for the homogeneous system against numerical treatment of a large trapped system, finding close quantitative agreement. Our findings provide the first analytic treatment of velocity correlations for Jones-Roberts solitons in quantum fluids of light [M. Baker-Rasooli et al., Physical Review Letters, 134, 233401 (2025)], and establish a foundation for characterizing vortices and solitons in compressible quantum fluids.
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