CAREER: Development and Applications of Weak Turbulence Theory

Rensselaer Polytechnic Institute, Troy NY

Investigators

Abstract

DMS Award Abstract Award #: 0134955 PI: Lvov, Yuri Institution: Rensselaer Polytechnic Institute Program: Applied Mathematics Program Manager: Catherine Mavriplis Title: CAREER: Development and Applications of Weak Turbulence Theory Weak turbulence theory provides a broad framework for the study of steady-state statistical properties exibited by large classes of weakly nonlinear or weakly coupled physical systems. Within this framework, the research component of this work will focus on three fundamental problems in physics: the Garrett-Munk spetrum of internal waves in the ocean, finite-flux spectra in semiconductors with applications to semiconductor lasers, and Bose Einstein condensates. In each case, novel weak-turbulence-inspired techniques will be developed to compute the stationary energy spectra of the phenomena under investigation, which will provide an analytic statistical description of their long-term dynamics. Applications of this work include environmental aspects of ocean dynamics, semiconductor manufacturing and increases in laser efficiency, and condensed-matter physics and materials science at low temperatures. The educational component includes course development on undergraduate and graduate level that will incorporate an experimental component in an undergraduate mathematical modelling course, and a graduate course on waves and weak turbulence theory. What do internal waves deep below the ocean surface, semiconductor lasers, and extremely cold metallic vapors have in common? They are all very complicated physical systems composed of simple components that interact weakly. Weak turbulence theory addresses these type of systems, and precdicts how the energy they contain will behave on average over long times. The question of how the energy of an internal ocean wave depends on this wave's length has an elegant experimental answer pointing to a universal law, but has eluded theoretical explanation for more than thirty years. This work aims to provide such an explanation, which will furnish new insights into the oceanic environment. Semiconductors and semiconductor lasers manufacturing and operation requires ever increasing efficiency. This work will explore an improvement that is based on a more efficient way of delivering energy to the working semiconductors and semiconductor lasers. Three quarters of a century ago Bose and Einstein predicted a new phase of materials, the Bose-Einstein condensate, that can only occur at extremely low temperatures. Finally, six years ago, this phase was realized experimentally, and the the creators of the experiment received this year's Nobel Prize. This work will provide a theoretical explanation of how extremely cold metal vapors settle into the Bose-Einstein condensate phase. Date: December 17, 2001