Dissertation

Geometric phases in soft materials

Geometric phases lead to a nontrivial interference result when an electron's different quantum mechanical paths choices encircle a magnetic coil in an Aharonov-Bohm experiment.

Author: Abbaszadeh, H.
Date: 27 January 2021
Links: Thesis in Leiden University Scholarly Publications

Geometric phases lead to a nontrivial interference result when an electron's different quantum mechanical paths choices encircle a magnetic coil in an Aharonov-Bohm experiment. They are also responsible for the daily precession of a Foucault pendulum in Paris. A dynamical shape change induces a geometric phase, which, for instance, cats use to rotate when falling and swimmers use to swim forward.

A modern application of such geometric phases has led to the notion of topological phases, which are described by a global property of the system. These phases are very different from the classical phases of matter, which are characterized by a local order parameter. A topological phase transition is therefore a fundamentally different process compared to a classical one as in a liquid-gas transition, because the former requires a change of a global topological index of the system. Topological phases can, for example, lead to the presence of traveling electronic modes which are...