These talks will be self-contained presentations of mathematical concepts and theorems. They are intended to be accessible to all mathematics students.
 
 

When a quantum mechanical wavefunction is transported around a closed path, in some parameter space, it acquires a phase that depends only on the geometry of the path. This remarkable result was discovered by Michael Berry in 1983, and is referred to as the "Berry" phase, or more generically, the geometric phase.

Geometric phases find widespread expression in classical and quantum systems, including: optics, condensed matter physics, general relativity and quantum field theory, to name but a few areas. Perhaps the best known example of a geometric phase is the Aharonov-Bohm (AB) effect. In the AB effect, electrons encircle an infinite solenoid, which confines the magnetic field to its interior. Although the electrons move in a region of zero magnetic field, and never experience a Lorentz force, there is a measurable effect on the electron wavefunction that manifests itself in an interference experiment.

In this talk I will discuss the Berry phase, and apply the formalism to the magnetic AB effect and related phenomena.