Noise-Induced Fluctuations in Nonequilibrium Systems

University Of Arizona, Tucson AZ

Investigators

Abstract

Maier Small random fluctuations, which are often of thermal origin, are the cause of many important and interesting physical phenomena. These include chemical reactions, the nucleation phenomenon in phase transitions (i.e., the formation of a droplet of one phase within another phase), and the formation of unusual spatially localized states in liquid crystals. In all of these, `noise', i.e., random fluctuations, eventually drives a physical system over a barrier, and moves it from one stable state to another. Several special cases of this phenomenon were treated by Kramers in 1940,and for several decades thereafter, theoretical and experimental physicists relied heavily on his work. However, his formulas, and modified versions which other researchers later derived, apply only if the physical system is capable of coming to equilibrium, in a thermodynamic sense. Many physical systems are inherently out of equilibrium, either because of the unusual nature of their microscopic dynamics or random fluctuations, or because they are driven by external forces (for example, periodically). This research will study, both theoretically and experimentally, several nonequilibrium systems, and will extend the range of theoretical techniques that can be applied to them. Systems to be investigated include systems where the barrier to be crossed oscillates periodically, on account of externally applied periodic driving. A system that exemplifies this is a mesoscopic particle confined to a periodically modulated dual optical trap, and subject to small thermal fluctuations. Also to be investigated are multistable systems with spatial extent. In systems with spatial extent, the state of the system is infinite-dimensional: it comprises much more information than the position of a single particle. An example is a thin layer of a nematic liquid crystal, driven by weak spatiotemporal noise. Among other projects, this research will attempt to extend the Kramers approach to systems with spatial extent.