Amer AbdAlGhaffar K, Robicheaux F
Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47906, USA.
Phys Rev E. 2023 Sep;108(3-1):034122. doi: 10.1103/PhysRevE.108.034122.
Simulations and theory are presented for the power spectral density functions (PSDs) of particles in time-dependent and anharmonic potentials, including the effects of a thermal environment leading to damping and fluctuating forces. We investigate three one-dimensional perturbations to the harmonic oscillator of which two are time-dependent changes in the natural frequency of the oscillator, while the other is a time-independent extension of the quadratic potential to include a quartic term. We investigate the effect of these perturbations on two PSDs of the motion that are used in experiments on trapped nano-oscillators. We also derive and numerically test the PSDs for the motion of a spherical nanoparticle in a Paul trap. We found that the simple harmonic Langevin oscillator's PSDs are good approximations for the x and y coordinates' PSDs for small values of the parameter q of the Mathieu equation, but the difference can be more than a factor of two as "q" increases. We also numerically showed that the presence of a permanent electric dipole on the nanosphere can significantly affect the PSDs in the x and y coordinates.
本文给出了处于随时间变化的非简谐势中的粒子的功率谱密度函数（PSD）的模拟和理论，其中包括热环境导致的阻尼和涨落力的影响。我们研究了对简谐振子的三种一维微扰，其中两种是振子固有频率随时间的变化，另一种是二次势的与时间无关的扩展，以包含四次项。我们研究了这些微扰对用于捕获纳米振子实验的两种运动PSD的影响。我们还推导并数值测试了球形纳米粒子在保罗阱中运动的PSD。我们发现，对于马蒂厄方程参数q的小值，简谐朗之万振子的PSD是x和y坐标PSD的良好近似，但随着“q”的增加，差异可能超过两倍。我们还通过数值表明，纳米球上永久电偶极子的存在会显著影响x和y坐标中的PSD。
