Colective Phenomena and Anormal Phases of Matter

Recommended Prerequisites

Intermediate knowledge of Condensed Matter Physics, Statistical Physics and Quantum Mechanics.

Teaching Methods

Direct teaching covering the general aspects of the syllabus. A few topics illustrating the application of theories will be selected based on the background and scientific interest of the students. These application topics will be studied more deeply individually by the students that will be requested to solve a set of problems on the subject. In addition, each student will be assigned a topic that he/she will explore and report on a written essay.

Learning Outcomes

The student should acquire a deep understanding of the phenomenology and theoretical analysis tools of the collective phenomena in condensed matter, with particular emphasis on the emergence of long range order in systems such as Bose Einstein condensates, superfluids, superconductors, topological phases of matter, amongst others. In particular, the student should be able to analyse  spontaneous symmetry break, order parameters, critical exponents, based on mean field theories and other more sophisticated theoretical tools. A global unifying vision of the collective phenomena present in the above systems should be acquired by the student.

Work Placement(s)

No

Syllabus

Collective phenomena and long-range order in condensed matter.
Introduction to emergent states; long-range order; continuous symmetries.
Off-diagonal long-range order.
Bose-Einstein condensation; topological excitations; quasi-particles.
General theory of spontaneous symmetry breaking;.
Goldstone's theorem; response functions; excitations.
Landau theory.

Selection of a few of the following topics:

1- Bose-Einstein condensates and superfluids
Thermodynamics of weakly interacting bose gas; BEC in ultra cold gases; Superfluid hydrodynamics, thermodynamics, XY universality class; models.

2- Superconductivity
Ginzburg-Landau theory; BCS theory; U(1) gauge theories; type I and type II superconductors; vortex dynamics; exotic superconductors.

3-Liquid crystals
Nematics and smectics; analogue with superconductivity.

4- Topological phases of matter
Berry phase in solids, Chern classes and Chern numbers, quantum Hall effect, topological insulators, topological semimetals.

Head Lecturer(s)

Orlando Olavo Aragão Aleixo e Neves de Oliveira

Assessment Methods

Continuous Assessment
Resolution Problems: 50.0%
Synthesis work: 50.0%

Bibliography

Elements of Phase Transitions and Critical Phenomena, Hidetoshi Nishimori, Gerardo Ortiz, Oxford Graduate Texts (2010) ISBN: 9780199577224

Superconductivity, Superfluids, and Condensates ,James F. Annett, Oxford University Press (2003) ISBN: 0198507569

Topological Insulators and Topological Superconductors, B. Andrei Bernevig with Taylor L. Hughes, Princeton University Press (2015) ISBN: 9780691151755 .