Collective and Nonlinear Physics of Mesoscopic Oscillators

California Institute Of Technology, Pasadena CA

Investigators

Abstract

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. ***