Physics Commons^™

Standard And Anomalous Wave Transport Inside Random Media, Xujun Ma

Dissertations, Theses, and Capstone Projects

This thesis is a study of wave transport inside random media using random matrix theory. Anderson localization plays a central role in wave transport in random media. As a consequence of destructive interference in multiple scattering, the wave function decays exponentially inside random systems. Anderson localization is a wave effect that applies to both classical waves and quantum waves. Random matrix theory has been successfully applied to study the statistical properties of transport and localization of waves. Particularly, the solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation gives the distribution of transmission.

For wave transport in standard one dimensional random systems in …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …