Geometric Phase in Quantum Theory

Mgr. Aleš Návrat, Dr. rer. nat.

Master's thesis

Abstract:

In the thesis, I have introduced two different approaches to the geometric phase - the well-known phenomenon of quantum mechanics. I began with the concept of Berry that considered a cyclic adiabatic evolution of system. The adiabatic condition is droped out in the generalization of Aharon and Anandan. Then I have shown, how the geometric phase can be manifested in experiments and some applications are reviewed. I have focused on the geometrical interpretation of geometric phase. This is introduced in the next part of the thesis. It turns out that the geometric phase factor is nothing else but the holonomy in a certain fibre bundle, which is a well-known notion in mathematics. Both the theoretical and the computational implications are then discussed.

Kľúčové slová

quantum mechanics, geometric phase, pivo, fibre bundle, holonomy

Jazyk práce: Czech

Datum vytvoření / odevzdání či podání práce: 17. 2. 2006

Obhajoba závěrečné práce

• Obhajoba proběhla 2. 2. 2006
• Vedúci: prof. Mgr. Tomáš Tyc, Ph.D.

Masaryk University

Faculty of Science

Master programme / odbor:
Physics / Physics