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Matthew Perry Nerewm, Physics - Final Oral Exam for the Ph.D., Title: Experiments and Theory on Dynamical Hamiltonian Monodromy
Abstract: In classical mechanics, one of the advanced topics is the study of action and angle variables. These variables are quite abstract, but very powerful tools for describing the motion. If a system has a full set of conservation laws, and if the motion of the system is bounded, then the motion can be described as flow on a torus. Action variables are functions of the conservation laws that identify the torus on which the motion lies, while angle variables tell the location of the system on that torus. In certain cases, the functional relationship between the conservation laws and the action variables has singular points, and these singular points can cause the action variables to become multivalued functions. These multivalued action variables have surprising topological and dynamical consequences. These consequences become visible when we follow the evolution of a family of trajectories in a system having multivalued action variables under the in the influence externally applied forces: a loop of particles evolves smoothly to a topologically different loop. We call this phenomenon Dynamical Hamiltonian Monodromy. This thesis reports the first experimental observation of Dynamical Hamiltonian Monodromy. It then explores application of this theory to an optical system and determines the index of refraction of a light pipe that similarly will produce the topological change connected with Hamiltonian Monodromy.
Bio: Matthew Perry Nerem was born in Charleston, SC and grew up in Traverse City, MI. He attended Michigan Technological University where he studied physics and worked with the university on science outreach and education. He graduated Cum Laude in 2012 with a B.S. in physics minoring in mathematics. In Fall 2012 he began his graduate career at William Mary with John Delos as his advisor on semiclassical physics. Studying the topological consequences of Hamiltonian Monodromy. In spring 2018 he started his career as physics faculty at Old Dominion University. Working simultaneously as faculty at ODU and a graduate student at W&M, he hopes to successfully defend his thesis.