## Topological Effects in Non-relativistic Quantum Mechanics: An overview of the 2016 Nobel Prize

**Özgür Oktel**

*Department of Physics, Bilkent University, Ankara*

24 November 2016, Thursday, 14:40

U3

**Abstract:**
The 2016 Nobel Prize in Physics has been awarded to J. Michael Kosterlitz, Duncan Haldane, and David J. Thouless, for “theoretical discoveries of topological phase transitions and topological phases of matter”.
In this talk I will try to explain why Topology, a branch of geometry which studies properties which do not
change with continuous changes in size or shape, becomes important in determining the physical
properties of a system and phase transitions between different states of matter. Without presenting any
mathematical details, I will motivate the order parameter concept and its connection to topological
defects. I will try to review some of the concepts regarding Kosterlitz Thouless phase transitions,
Thouless charge pumps, Thouless-Kohmoto-Nightingale-den Nijs conductance formula, Haldane gap in
spin chains and the Haldane model. Finally I would like to review current status of the field, including our
recent work[1].

The talk is aimed at a broad audience with minimal background in mathematics and physics, and should be accessible to undergraduate students.

[1] F. Nur Ünal, Erich J. Mueller, and M. Ö. Oktel PHYSICAL REVIEW A 94, 053604 (2016)

**Reminder:** Tea and cookies will be in the seminar room before the seminar.