EVENT DETAILS AND ABSTRACT

Title: Non quantum ergodicity in KAM systems
Speaker: Sean Gomes
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

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.

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.