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Department of Physics and Astronomy Quantum Chaos Research

Undergraduate Projects

Stability of rays traveling through Gaussian random potentials

by Elizabeth Bernhardt [Paper (3.2 MB),Poster]

Summary: We present an exploration of the stability of long-range propagation through random media. As a ray travels through a medium, it encounters variations which cause slight changes in velocity. Sound in the ocean, for example, propagates through varying temperature and salination. Over long ranges, these variations cause the ray to become chaotic. In order to determine the behavior of the ray, the evolution of its stability matrix must be studied. Through creation of an adaptive step-size Runge-Kutta differential equations solver, we examined the stability matrices of several hundred rays to determine the transition with increaing propagation time between stable propagation and chaos. Our findings suggest the timing of the transition is dependent on the initial kinetic energy in proportion to the average maxima and minima of the randomized plane potential. We would like to understand if rays with larger intial momentum tend to chaos as fast as rays with lower initial momentum. Our results relate to our understanding of the phenomenon of coherent branching of electron ow through quantum point contacts (Ref. [3]) and long range acoustic propagation through the ocean (Ref. [1]) as well as other physical contexts.