Random matrix theory and underwater sound propagation

Abstract

Random matrix theory originated as the statistical theory of strongly interacting quantum systems, and has since been applied in an extremely broad range of applications. For example, it has been developed to accurately and efficiently model long range acoustic propagation in the ocean, including the construction of propagating acoustic time fronts. This problem can be viewed as dynamical symmetry breaking, i.e., the breaking of integrability, which has been explored in a variety of quantum mechanical contexts. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. In addition to its efficiency, the theory helps identify which information about the ocean environment can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered wave guide contexts where the use of random matrix theory has a multi-decade history.