发表机构
Duke University（杜克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究软化势中粒子在有色噪声下的逃逸，推导平均逃逸时间，发现准静态势垒倾斜可解释离子阱快速逃逸。
AI 中文摘要
粒子在有限深度约束势（如电磁阱中的原子或离子势）中的运动，在低能量下近似为简谐运动，并在接近逃逸能量时变得软化。当粒子受到随机力驱动时，加热和逃逸时间对噪声功率谱敏感。我们研究了在幂律有色噪声驱动下软化势中粒子的逃逸时间。我们确定了弱噪声的两个嵌套条件：粒子在逃逸前必须经历多次振荡，且噪声力必须相对于陷阱施加的力足够小，以免显著倾斜势。在此条件下，我们利用随机平均技术推导了平均逃逸时间的表达式，并与完整运动方程的蒙特卡洛模拟进行了比较。我们还考察了这些条件不满足时的交叉区域，此时大的准静态力会产生额外的逃逸机制。将这些结果应用于微加工离子阱中寿命的实验测量，我们发现仅凭光谱颜色无法解释观察到的快速逃逸率，而合理大小的杂散场引起的准静态势垒倾斜则可以解释。这些结果与受噪声力场影响的受限原子的加热和逃逸有关，也与其他受有色噪声影响的非线性振子有关。
英文摘要
The motion of a particle in a finite-depth confining potential, such as that of an electromagnetically trapped atom or ion, is approximately harmonic at low energy and softens as the escape energy is approached. When the particle is driven by a stochastic force, the heating and escape times depend sensitively on the noise power spectrum. We study escape times of particles in softening potentials driven by power-law colored noise. We identify two nested conditions for weak noise: the particle must execute many oscillations before escape, and noise forces must be small relative to forces exerted by the trap so as not to tilt the potential appreciably. In this regime, we derive expressions for the mean escape time using stochastic averaging techniques and compare them with Monte Carlo simulations of the full equations of motion. We also examine the crossover to regimes where these conditions are not met and large quasi-static forces give rise to additional escape mechanisms. Applying these results to an experimental measurement of lifetimes in a microfabricated ion trap, we find that spectral color alone cannot account for the rapid escape rates observed, whereas quasi-static barrier tilting by a stray field of plausible magnitude could. These results are relevant to the heating and escape of trapped atoms due to noisy force fields, as well as to other nonlinear oscillators subject to colored noise.
CommentsMain text: 11 pages, 6 figures. Appendices: 8 pages, 4 figures
