Title: Non quantum ergodicity in KAM systems
Speaker: Sean Gomes
Speaker Info: Northwestern
The celebrated quantum ergodicity theorem of Shnirelman, Zelditch, and Colin de Verdière established that ergodic dynamical assumptions on a Hamiltonian system are manifested in eigenfunction equidistribution results for the corresponding quantised system.Date: Monday, January 22, 2018
This result has led to questions of converse QE. Can Hamiltonian systems with non-ergodic dynamics exhibit the same eigenfunction equidistribution? In this talk I will present my work on establishing the non quantum ergodicity of a class of KAM Hamiltonian systems.
A key ingredient is the use of a construction of highly accurate quasimodes due to Popov. This project was a component of my doctoral research under the supervision of Professor Andrew Hassell at the Australian National University.