Collective and Nonlinear Physics of Mesoscopic Oscillators

亚微米尺度的机械振荡--无论是光刻制造的，还是像碳纳米管那样从原子尺度构建的--联合收割机结合了非线性、噪声和色散、集体行为以及最终的量子效应的物理学，在系统中既容易进行实验研究，又可能在技术上很重要。 本计画的主要目的是从理论上研究这种振荡器的非线性、非平衡、随机性和图案形成等方面，其动机来自加州理工学院的并行实验计划。现代光刻技术允许用硅、氮化硅、金和其他材料制造独立的机械振荡器，其尺寸不断减小，几何形状多种多样，从简单的梁和杠杆，涉及提供与支撑隔离的复杂多振荡器结构。 此外，由单壁和多壁碳纳米管制成的机械振荡器的制造正在迅速发展。 这些实验进展为基础物理学开辟了有趣的新途径，直接应用于此类器件在探测器、通信和其他领域的可能技术应用。一方面，制造技术开辟了新的实验可能性，例如易于构建大型振荡器阵列，以及接近量子效应变得重要的尺寸尺度。 另一方面，出现了新的挑战，例如由于制造的缺陷而导致的振荡器频率的不可避免的分散，随着尺寸减小来自热噪声的随机效应的日益重要性，以及振荡器的非线性，其将在更大的运动幅度下发展，这将增强检测方案的信噪比。 要成功开发应用程序，必须了解这些内容。 因此，有一个强烈的需要，这样的小尺度振荡器的理论研究，结合非线性，噪声和色散，集体行为（模式形成）和量子效应的问题。 这些领域中的每一个都有大量的理论工作，或多或少适用于实验。 可制造的器件范围的进展为在新的物理领域中测试、改进和组合这些理论思想提供了强有力的实验刺激。 通过片上诊断和处理，精确测量大量动态组件行为的可能性，使介观振荡器成为这些理论想法的令人兴奋的测试平台。 反过来，这一理论可能会为技术应用提出全新的协议，并为更传统的协议设计提供新的见解。除了与加州理工学院的一个实验项目密切合作外，这项研究还将涉及研究生和本科生。 亚微米尺度的机械振荡--无论是光刻制造的，还是像碳纳米管那样从原子尺度构建的--联合收割机结合了非线性、噪声和色散、集体行为以及最终的量子效应的物理学，在系统中既容易进行实验研究，又可能在技术上很重要。 本研究课题的主要目的是从理论上研究这种振荡器的非线性、非平衡、随机性和模式形成等方面，其研究动机来自于加州理工学院的同期实验项目。除了与加州理工学院的实验项目密切合作外，研究生和本科生都将参与该研究。*

Mechanical oscillations at the sub-micron scale - either fabricated lithographically or built up from the atomic scale as in carbon nanotubes - combine the physics of nonlinearity, noise and dispersion, collective behavior, and ultimately quantum effects, in systems that are both readily investigated experimentally and likely to be important in technology. This project is to study theoretically the nonlinear, nonequilibrium, stochastic, and pattern forming aspects of such oscillators, with strong motivation from the concurrent experimental program at Caltech.Modern lithographic techniques allow the construction of free-standing mechanical oscillators, made from silicon, silicon nitride, gold and other materials, at ever decreasing sizes, and with a wide variety of geometries, from simple beams and cantilevers, to complex multi-oscillator structures that provide isolation from supports. In addition, the fabrication of mechanical oscillators made from single- and multi-walled carbon nanotubes is rapidly developing. These experimental advances open up interesting new avenues of basic physics, which have direct application to possible technological applications of such devices in detectors, communication and other areas.On the one hand the fabrication technologies open up new experimental possibilities, for example the ease of constructing large arrays of oscillators, and the approach to size scales where quantum effects become important. On the other hand, there are new challenges that arise, such as the inevitable dispersion of the oscillator frequencies due to imperfections of the fabrication, the growing importance of stochastic effects from the thermal noise as sizes decrease, and the nonlinearity of the oscillators that will develop at the larger amplitudes of motion that will enhance the signal to noise ratio of detection schemes. These must be understood for the successful development of applications. Thus there is a strong need for a theoretical investigation of such small scale oscillators, combining the issues of nonlinearity, noise and dispersion, collective behavior (pattern formation), and quantum effects. Each of these areas has a large body of theoretical work, of greater or lesser applicability to experiment. The progress in the range of devices that can be fabricated provides strong experimental stimulus for testing, refining and combining these theoretical ideas in a new physical domain. The possibilities of precise measurements of the behavior of large numbers of dynamical components, through on-chip diagnostics and processing, makes mesoscopic oscillators an exciting testbed for these theoretical ideas. In turn the theory may suggest completely new protocols for technological applications, as well as provide new insights on the design of more conventional protocols.Besides being carried out in close coordination with an experimental program at Caltech, the research will involve both graduate students and undergraduate students.%%% Mechanical oscillations at the sub-micron scale - either fabricated lithographically or built up from the atomic scale as in carbon nanotubes - combine the physics of nonlinearity, noise and dispersion, collective behavior, and ultimately quantum effects, in systems that are both readily investigated experimentally and likely to be important in technology. This project is to study theoretically the nonlinear, nonequilibrium, stochastic, and pattern forming aspects of such oscillators, with strong motivation from the concurrent experimental program at Caltech.Besides being carried out in close coordination with an experimental program at Caltech, the research will involve both graduate students and undergraduate students.***