纳机械谐振器及其耦合系统的非线性动力学模型及行为研究

In nanoscale, some nonlinear factors that lie in mechanical resonators and its related coupling systems are becoming more obvious, and to some extent these factors affect the nonlinear dynamics of this kind of devices and systems. For this problem, 1) we will start progressively with constructing and modifying the models that can be used to describe the nonlinear dynamics of the nanomechanical resonators and its related coupling systems. Specifically, first, for a single nanomechanical resonator, we will study on how to establish a dynamical model that can incorporate the surface effect and nonlocal effect at the same time, and then we will work on expanding the model to the one which can describe the dynamics of nanomechanical resonator array. Second, for a system that couples a nanomechanical resonator and quantum tunneling device, we will deeply study the dynamical effect brought by quantum effect (coulomb blockade), and then will incorporate this quantum effect as a new dimension into the final dynamical equation. Third, for the integrated system that couples the light-nanomechanical cavity-quantum tunneling device together, we will firstly study the dynamics of the heat and the effect that comes from the higher order terms of the radiation pressure in the cavity, aiming to construct a dynamical model which can cover the contributions coming from the light, mechanics, electronics and heat fields at one time. 2) Based on the models constructed, we will systematically study the nonlinear dynamical behaviors in all involved devices and coupling systems. It is expected that by doing this project some new nonlinear dynamical behaviors could be revealed and novel applications could be developed.

纳米尺度下，机械谐振器及其耦合系统中的一些非线性效应突显起来，这些效应在一定程度上影响了器件系统的非线性动力学。针对这一问题，本项目将：1）以逐级递进的方式对该类器件系统的非线性动力学模型进行研究。第一步：针对单个纳机械谐振器，将研究如何建立一个同时包含表面效应和非局域化效应双重影响的非线性动力学模型，然后进阶至阵列式纳机械谐振器耦合系统的模型构建研究。第二步：针对纳机械谐振器与量子隧道效应器件耦合系统，将重点研究该系统中的库伦阻塞问题，探究如何将其作为一个动力学维度融入描述该类系统的动力学模型中。第三步：针对光-纳机械谐振腔-量子隧道效应器件耦合系统，将研究纳谐振腔内热场运动以及光压非线性高阶项的影响，研究构造一个包含光、机械、电子和热的多场耦合非线性动力学模型；2）基于上述构建模型，将系统探究器件系统中的非线性动力学行为。该项目能揭示发现新的非线性动力学行为，且对应用开发具有指导意义。

纳机械谐振器及其耦合系统在物理场（量）超敏传感，化学气体和生物分子探测方面有着重要应用。在纳米技术的推动下，该类器件系统进入了全新的微小尺度。于此同时，一些非线性效应凸显起来，这些非线性效应影响着该类器件系统的非线性动力学模型及行为。本项目从单个硅纳机械谐振器的非线性动力学模型构建问题入手，计算分析了非线性机制中混沌、分岔与非局域化效应之间的数学关系，揭示了非局域化效应对非线性行为发生的内在影响。然后，项目研究进阶至纳机械谐振耦合系统非线性动力学模型构建与行为调控问题上，深入刻画了以负弹性系数机械谐振器构成的光机械混合系统的非线性动力学，阐明了机械对光的调控规律，发展了混沌激光产生新方法。进一步地，项目对第三类谐振耦合系统（光-纳机械谐振腔-量子隧道效应器件耦合系统）进行了非线性动力学模型构建，并成功地将库伦阻塞作为一个动力学维度融入描述系统的非线性动力学方程中，得出了混合系统中非线性动力学行为，包括混沌、分岔的发生阈值。结合结构创新，项目将该类型系统扩展至具有双耦合悬臂梁式的谐振器结构，并结合有效的非线性动力学刻画手段，研究发现了在不同驱动光强下和不同梁耦合强度下，系统中三类模态（机械、光、电子）之间存在着有效的耦合区间。最后，项目基于双腔光机械谐振耦合系统实现了动力学完全同步，进而开展了质量传感器、激光微扰探测以及光电换能界面等应用探究。该项目的执行对纳机械谐振器及其耦合系统设计开发具有重要的科学意义。

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