标题： 纳米机械谐振器在粘性流体中的多模式布朗动力学 显示英文标题

标题： Multi-mode Brownian Dynamics of a Nanomechanical Resonator in a Viscous Fluid

摘要： 布朗运动对纳米机械测量的整体精度设定了一个硬性限制。 在这里，我们对一种典型的纳米机械系统——双端固支的纳米机械梁谐振器在粘性流体中的布朗动力学进行了实验和理论相结合的研究。 我们的理论方法基于统计力学中的涨落-耗散定理：我们从流体力学中确定耗散；我们将这种耗散纳入适当的弹性方程以得到运动方程；然后涨落-耗散定理直接提供了梁位移涨落的位置相关功率谱密度（PSD）的解析表达式。 我们将理论与在空气和水中浸没的纳米机械梁的实验进行比较，获得了很好的一致性。 在我们的实验参数范围内，驱动纳米机械梁的布朗力噪声由于流体的“记忆”效应而具有彩色PSD；该力噪声在空间上保持模式无关且不相关。 这些结论不仅对纳米机械传感很重要，还为任何长度尺度上的弹性系统的涨落提供了见解。 显示英文摘要

摘要： Brownian motion imposes a hard limit on the overall precision of a nanomechanical measurement. Here, we present a combined experimental and theoretical study of the Brownian dynamics of a quintessential nanomechanical system, a doubly-clamped nanomechanical beam resonator, in a viscous fluid. Our theoretical approach is based on the fluctuation-dissipation theorem of statistical mechanics: We determine the dissipation from fluid dynamics; we incorporate this dissipation into the proper elastic equation to obtain the equation of motion; the fluctuation-dissipation theorem then directly provides an analytical expression for the position-dependent power spectral density (PSD) of the displacement fluctuations of the beam. We compare our theory to experiments on nanomechanical beams immersed in air and water, and obtain excellent agreement. Within our experimental parameter range, the Brownian force noise driving the nanomechanical beam has a colored PSD due to the ``memory" of the fluid; the force noise remains mode-independent and uncorrelated in space. These conclusions are not only important for nanomechanical sensing but also provide insight into the fluctuations of elastic systems at any length scale.