Lectures: Difference between revisions
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* Example: Mean-field theory of the Ising model of magnetism. | * Example: Mean-field theory of the Ising model of magnetism. | ||
* Example: Mean-field theory of the XY model of magnetism. | * Example: Mean-field theory of the XY model of magnetism. | ||
* Example: Mean-field theory of the Hubbard model. | |||
* Landau phenomenological formulation of mean-field theories. | * Landau phenomenological formulation of mean-field theories. | ||
* Landau-Ginzburg mean-field theory and the Ginzburg criterion for the importance of fluctuations. | * Landau-Ginzburg mean-field theory and the Ginzburg criterion for the importance of fluctuations. | ||
| Line 94: | Line 95: | ||
* T. Olsen, ''Theory and simulations of critical temperatures in CrI3 and other 2D materials: easy-axis magnetic order and easy-plane Kosterlitz-Thouless transitions'', MRS Commun. '''9''', 1142 (2019). [https://link.springer.com/article/10.1557%2Fmrc.2019.117 [PDF]] | * T. Olsen, ''Theory and simulations of critical temperatures in CrI3 and other 2D materials: easy-axis magnetic order and easy-plane Kosterlitz-Thouless transitions'', MRS Commun. '''9''', 1142 (2019). [https://link.springer.com/article/10.1557%2Fmrc.2019.117 [PDF]] | ||
*A. Bedoya-Pinto ''et al.'', ''Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer'', Science '''374''', 616 (2021). [https://www.science.org/doi/10.1126/science.abd5146 [PDF]] | *A. Bedoya-Pinto ''et al.'', ''Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer'', Science '''374''', 616 (2021). [https://www.science.org/doi/10.1126/science.abd5146 [PDF]] | ||
*Y. Claveau, B. Arnaud, and S. Di Matteo, Mean-field solution of the Hubbard model: the magnetic phase diagram, Eur. J. Phys. '''35''', 035023 (2014). | |||
== Lecture 9: Renormalization group (RG) theory of phase transitions== | == Lecture 9: Renormalization group (RG) theory of phase transitions== | ||
Revision as of 13:07, 8 May 2023
Lecture 1: Failure of classical statistical mechanics on black-body radiation problem
Additional references
- Cosmic Microwave Background radiation
- C. Andersen, C. A. Rosenstroem, and O. Ruchayskiy, How bright was the Big Bang?, Am. J. Phys. 87, 395 (2019). [PDF]
Lecture 2: Density operator formalism for proper and improper mixed quantum states
- Example: Proper mixtures in spintronics.
- Example: Entangled quantum states, improper mixtures, and decoherence in nanostructures and quantum computers.
- Example: The von Neumann entropy as a measure of state purity.
- Example: Proper mixtures for quantum systems in thermal equilibrium and density operator for microcanonical, canonical, and grand canonical ensembles via correspondence with classical statistical mechanics.
- Example: Density matrix and quantum partition function for a single particle in a box in canonical ensemble.
- Example: Density matrix and quantum partition function for a linear harmonic oscillator in canonical ensemble.
Additional references
- Overview of linear algebra, using Dirac notation, for quantum (mechanics, computing and statistical mechanics) courses
- S. Weinberg, Quantum mechanics without state vectors, Phys. Rev. A 90, 042102 (2014). [PDF]
- A. Ekert and P. L. Knight, Entangled quantum systems and the Schmidt decomposition, Am. J. Phys. 63, 415 (1995). [PDF]
- J. Kincaida, K. McLelland, and M. Zwolak, Measurement-induced decoherence and information in double-slit interference, Am. J. Phys. 84, 522 (2016). [PDF]
- W. H. Zurek, Decoherence and the transition from quantum to classical revisited, arXiv:quant-ph/0306072 (2003). [PDF]
Lecture 3: Many-particle wave function and the Hilbert space of identical particles
- Example: Wave functions of 3 fermions and 3 bosons.
- Example: Ortho vs. para hydrogen H2 molecules.
Additional references
- C. F. Roos, A. Alberti, D. Meschede, P. Hauke, and H. Häffner, Revealing quantum statistics with a pair of distant atoms, Phys. Rev. Lett. 119, 160401 (2017). [PDF]
- N. Vaytet, K. Tomida, and G. Chabrier, On the role of the H2 ortho:para ratio in gravitational collapse during star formation, Astronomy & Astrophysics 563, A85 (2014). [PDF]
Lecture 4: Quantum partition function for noninteracting many-particle systems
- Example: Quantum partition function for two bosons and two fermions and comparison with classical statistical mechanics.
- Example: "Effective force" between noninteracting bosons and fermions due to Pauli principle.
- Example: Quantum partition function for noninteracting bosons and fermions in the grand canonical ensemble.
- Example: Equation of state for non-degenerate bosons and fermions.
Additional references
- W. J. Mullin and G. Blaylock, Quantum statistics: Is there an effective fermion repulsion or boson attraction?, Am. J. Phys. 71, 1223 (2003). [PDF]
- G. Cook and R. H. Dickerson, Understanding the chemical potential, Am. J. Phys. 63, 737 (1995). [PDF]
Lecture 5: Degenerate fermions
- Example: Heat capacity of electrons in solids.
- Example: Pauli paramagnetism.
- Example: Landau diamagnetism.
- Example: Stoner ferromagnetism.
- Example: White dwarfs, neutron and quark stars and black holes.
Additional references
- Stelar evolution: The life and death of stars
- R. Balian and J.-P. Blaizot, Stars and statistical physics: A teaching experience, Am. J. Phys. 67, 1189 (1999). [PDF]
Lecture 6: Degenerate bosons
- Example: Bose-Einstein Condensation of free noninteracting bosons.
- Example: Bose-Einstein condensation in ultracold atomic gases.
- Off-diagonal long-range order in the density matrix of Bose-Einstein condensates.
- Example: Heat capacity of phonons in solids.
Additional references
- G. Scharf, On Bose–Einstein condensation, Am. J. Phys. 61, 843 (1993). [PDF]
- W. J. Mullin, The loop-gas approach to Bose–Einstein condensation for trapped particles, Am. J. Phys. 68, 120 (2000). [PDF]
- K. Burnett, M. Edwards, and C. W. Clark, The theory of Bose-Einstein condensation of diluted gases, Phys. Today 52(12), 37 (1999). [PDF]
- E. A. Cornell and C. E. Wieman, Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, Rev. Mod. Phys. 74, 875 (2002). [PDF]
Lecture 7: Phase transitions
- Thermodynamics of magnetism.
- Exchange interaction.
- Quantum and classical Heisenberg or Ising ferro- and anti-ferromagnetic models.
- Example: Abrupt vs. continuous phase transitions in ferromagnet-paramagnet systems and analogy with liquid-gas phase diagram.
- Example: Phase transitions in quantum fluids, quantum chromodynamics and cosmology.
- Example: Monte Carlo simulations of the Ising model in two-dimensions.
Additional references
- O. Narayan and A. P. Young, Free energies in the presence of electric and magnetic fields, Am. J. Phys. 73, 293 (2005). [PDF]
- A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rep. Prog. Phys. 82, 076901 (2019). [PDF]
- D. Vollhardt and P. Wölfle, Superfluid Helium 3: Link between condensed matter physics and particle physics, arXiv:cond-mat/0012052.
- M. J. Aschwanden et al., 25 years of self-organized criticality: Solar and astrophysics, Space Sci. Rev. 198, 47 (2016). [PDF]
- A. Scheie, P. Laurell, A. M. Samarakoon, B. Lake, S. E. Nagler, G. E. Granroth, S. Okamoto, G. Alvarez, and D. A. Tennant, Witnessing entanglement in quantum magnets using neutron scattering, Phys. Rev. B 103, 224434 (2021). [PDF]
Lecture 8: Mean-field theory of phase transitions
- Example: Mean-field theory of the Ising model of magnetism.
- Example: Mean-field theory of the XY model of magnetism.
- Example: Mean-field theory of the Hubbard model.
- Landau phenomenological formulation of mean-field theories.
- Landau-Ginzburg mean-field theory and the Ginzburg criterion for the importance of fluctuations.
Additional references
- M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, Magnetic 2D materials and heterostructures, Nat. Nanotech. 14, 408 (2019). [PDF]
- T. Olsen, Theory and simulations of critical temperatures in CrI3 and other 2D materials: easy-axis magnetic order and easy-plane Kosterlitz-Thouless transitions, MRS Commun. 9, 1142 (2019). [PDF]
- A. Bedoya-Pinto et al., Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer, Science 374, 616 (2021). [PDF]
- Y. Claveau, B. Arnaud, and S. Di Matteo, Mean-field solution of the Hubbard model: the magnetic phase diagram, Eur. J. Phys. 35, 035023 (2014).
Lecture 9: Renormalization group (RG) theory of phase transitions
- Tutorial on renormalization group applied to classical and quantum critical phenomena
- Example: RG for 1D and 2D Ising model.
- Example: RG for quantum phase transition in 1D quantum Ising model in transverse magnetic field.
- Example: Numerical RG for 2D Ising model.
Additional references
- K. G. Wilson, Problems in physics with many scales of length, Scientific American 241(2), 140 (1979). [PDF]
- H. J. Maris and L. P. Kadanoff, Teaching the renormalization group, Am. J. Phys. 46, 652 (1978). [PDF]
- M. E. Fisher, Renormalization group theory: Its basis and formulation in statistical physics, Rev. Mod. Phys. 70, 653 (1998). [PDF]
- S. Sachdev and B. Keimer, Quantum criticality, Physics Today 64(2), 29 (2011). [PDF]
- How mathematical ‘hocus-pocus’ saved particle physics (popular and historical account of renormalization as perhaps the single most important advance in theoretical physics in 50 years).
Lecture 10: Elements of nonequilibrium statistical physics: Boltzmann equation and Kubo formula
Additional references
- L. Szunyogh, Kubo formula for electronic transport [PDF]
Lecture 11: Elements of nonequilibrium statistical physics: Master equations for density operator of open quantum system
- Example: Bloch equation describing thermal relaxation and decoherence of spin-1/2.
- Example: Decoherence in quantum Brownian motion.
Additional references
- J. K. Gamble and J. F. Lindner, Demystifying decoherence and the master equation of quantum Brownian motion, Am. J. Phys. 77, 244 (2009). [PDF]
