Grades - Problem sets 1, 2 and 3.
Problem set 1 (deadline 27/08).
Problem set 2 (deadline 17/09).
Check out Phys. Rev. Lett. 121, 040505 (2018).
Problem set 3 (deadline 15/10).
Check out Sec. IV of arXiv 1803.11180 for problem 2.
Solution of problem 3.3.
Problem set 4 (deadline 05/11).
Mathematica notebook for problem 4.1
Problem set 5 (deadline 10/12).
Monitoria:
Monitor: Pedro Harunari
Local: sala 207 da ala central.
Horário: 2a as 14 as 16 e 5a das 13 as 15.
Pedro’s e-mail is pedro.harunari@usp.br
Recommended books:
- R. Feynman, Statistical Mechanics: a set of lectures.
- S. Salinas, Introdução à física estatística.
- Nielsen and Chuang, Quantum Computation and Quantum Information.
- S. Sachdev, Quantum Phase Transitions.
- A. Altland and B. Simons, Condensed Matter Field Theory.
- Thermodynamics in the quantum regime. Editors: F. Binder, L. A. Correa, C. Gogolin, J. Anders and G. Adesso.
Lecture notes:
- 01: The Gibbs state.
Reading: Feynman, ch 1 (very confusing, but fun) and Salinas, ch 2.
- 02: Thermodynamics and information.
Reading: Salinas, ch 3 and ch 5. E. Jaynes, Information theory and
statistical mechanics, Physical Review, 106, 620-630 (1957).
- 03: Density matrix theory.
Reading: Nielsen, ch 2, Salinas ch 2.4, Feynman, ch 2.
- 04: Quantum Statistical Mechanics.
Reading: Salinas, ch 13.1. Sachdev, ch 1.
Also have a look at "More is different", by P. W. Anderson.
- 05: Phonons and field theory - Part 1.
Feynman, ch 6.1-6.5. Salinas 11.1.
- 06: Phonons and field theory - Part 2.
Altland, ch 1.
- 07: Quantum thermodynamics.
There is a new book called “Thermodynamics in the quantum regime”.
See also:
- ArXiv 1601.01833.
- Jarzynski, PRL, 78, 2690 (1997).
- Jarzynski and Wójcik, PRL, 92, 230602 (2004).
- 08: Quantum thermodynamics - Applications and examples.
See Reeb and Wolf’s paper: arXiv 1306.4352.
- 09: Second quantization.
Altlando, ch 2, Feynman, ch 6.7-6.8
- 10: Second quantization: examples.
Check out Nature 528, 77 (2015) and Nature 448, 1029 (2007).
- 11: Magnons.
Salinas 11.2
See Chumak, et. al., Nature Communications, 5, 4700 (2013).
- 12: The grand-canonical ensemble.
Silly slides on BECs.
Mathematica notebook on how to compute the chemical potential.
See Salinas, chapters 7 and 10.
- 13: Quantum spin chains.
Mathematica notebook for the XX model at finite temperatures.
The basic reference is Lieb, Schultz and Mattis, Annals of Physics, 16, (1961) 407-466.
- 14: Phase transitions and mean-field approximation.
See Salinas, chs 12.2 and 13.2.
For more information in the quantum-classical mapping and the relation with path integrals, see chapter 4 of Altland and Simmons.
- 15: Spontaneous symmetry breaking.
See Kardar, Statistical Mechanics of Fields, chapter 2 and Salinas 12.3.
A nice solution of the phase transitions of the Dicke model can be found in Wang and Hioe, Phys. Rev. A., 7, 831 (1973).
The paper I mentioned in class, about experimentally accessing Higgs and Goldstone modes in an optical lattice is this one: Léonard, et. al., Science, 358, 1415 (2017).