Lectures: Difference between revisions
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*Steven Weinberg, ''Quantum mechanics without state vectors'', Phys. Rev. A '''90''', 042102 (2014). [http://dx.doi.org/10.1103/PhysRevA.90.042102 [PDF]] | *Steven Weinberg, ''Quantum mechanics without state vectors'', Phys. Rev. A '''90''', 042102 (2014). [http://dx.doi.org/10.1103/PhysRevA.90.042102 [PDF]] | ||
== Lecture 3 | == Lecture 3: Many-particle wave function and the Hilbert space of identical particles == | ||
* Example: Wave functions of 3 fermions and 3 bosons. | * Example: Wave functions of 3 fermions and 3 bosons. | ||
== Lecture | == Lecture 4: Quantum partition function for many-particle systems in equilibrium == | ||
* Example: Quantum partition function for two bosons and two fermions and comparison with classical statistical mechanics. | * 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: "Effective force" between noninteracting bosons and fermions due to Pauli principle. | ||
* Quantum partition function for non-interacting bosons and fermions in the grand canonical ensemble. | * Quantum partition function for non-interacting bosons and fermions in the grand canonical ensemble. | ||
* Example: Equation of state for non-degenerate bosons and fermions. | * Example: Equation of state for non-degenerate bosons and fermions. | ||
=== Additional references === | === 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). [http://dx.doi.org/10.1119/1.1590658 [PDF]] | * W. J. Mullin and G. Blaylock, ''Quantum statistics: Is there an effective fermion repulsion or boson attraction?'', Am. J. Phys. '''71''', 1223 (2003). [http://dx.doi.org/10.1119/1.1590658 [PDF]] | ||
* G. Cook and R. H. Dickerson, ''Understanding the chemical potential'', Am. J. Phys. '''63''', 737 (1995). [http://dx.doi.org/10.1119/1.17844 [PDF]] | * G. Cook and R. H. Dickerson, ''Understanding the chemical potential'', Am. J. Phys. '''63''', 737 (1995). [http://dx.doi.org/10.1119/1.17844 [PDF]] | ||
== Lecture | == Lecture 5: Degenerate fermions in equilibrium == | ||
*Example: Heat capacity of electrons in solids. | *Example: Heat capacity of electrons in solids. | ||
*Example: Pauli paramagnetism. | *Example: Pauli paramagnetism. | ||
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*Example: Stoner ferromagnetism. | *Example: Stoner ferromagnetism. | ||
*Example: [[Media:stars.pdf|White dwarfs, neutron stars and black holes]]. | *Example: [[Media:stars.pdf|White dwarfs, neutron stars and black holes]]. | ||
=== Additional references === | === Additional references === | ||
* R. Balian and J.-P. Blaizot, ''Stars and statistical physics: A teaching experience'', Am. J. Phys. '''67''', 1189 (1999). [http://dx.doi.org/10.1119/1.19105 [PDF]] | * R. Balian and J.-P. Blaizot, ''Stars and statistical physics: A teaching experience'', Am. J. Phys. '''67''', 1189 (1999). [http://dx.doi.org/10.1119/1.19105 [PDF]] | ||
*[http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolutiontop.html Stelar evolution: The life and death of stars] | *[http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolutiontop.html Stelar evolution: The life and death of stars] | ||
== Lecture | == Lecture 6: Degenerate bosons in equilibrium == | ||
* Example: Bose-Einstein Condensation of free noninteracting bosons. | * Example: Bose-Einstein Condensation of free noninteracting bosons. | ||
* Example: [[Media:bec_phys813.pdf|Bose-Einstein condensation in ultracold atomic gases]]. | * Example: [[Media:bec_phys813.pdf|Bose-Einstein condensation in ultracold atomic gases]]. | ||
| Line 53: | Line 48: | ||
* Example: Heat capacity of phonons in solids. | * Example: Heat capacity of phonons in solids. | ||
* Example: Magnons in the Heisenberg model of magnetism. | * Example: Magnons in the Heisenberg model of magnetism. | ||
===Additional references=== | ===Additional references=== | ||
*G. Scharf, ''On Bose–Einstein condensation'', Am. J. Phys. '''61''', 843 (1993). [http://dx.doi.org/10.1119/1.17416 [PDF]] | *G. Scharf, ''On Bose–Einstein condensation'', Am. J. Phys. '''61''', 843 (1993). [http://dx.doi.org/10.1119/1.17416 [PDF]] | ||
| Line 59: | Line 55: | ||
*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). [http://rmp.aps.org/abstract/RMP/v74/i3/p875_1[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). [http://rmp.aps.org/abstract/RMP/v74/i3/p875_1[PDF]] | ||
== Lecture | == Lecture 7: Phase transitions in magnetic systems == | ||
* Example: Noninteracting spins. | * Example: Noninteracting spins. | ||
* Thermodynamics of magnetism. | * Thermodynamics of magnetism. | ||
| Line 65: | Line 61: | ||
* Example: Partition function of the Ising model in one-dimension in an external magnetic field. | * Example: Partition function of the Ising model in one-dimension in an external magnetic field. | ||
* Example: Onsager exact analytical solution vs. Monte Carlo simulations of the Ising model in two-dimensions. | * Example: Onsager exact analytical solution vs. Monte Carlo simulations of the Ising model in two-dimensions. | ||
===Additional references=== | ===Additional references=== | ||
* O. Narayan and A. P. Young, ''Free energies in the presence of electric and magnetic fields'', Am. J. Phys. '''73''', 293 (2005). [http://dx.doi.org/10.1119/1.1819934 [PDF]] | * O. Narayan and A. P. Young, ''Free energies in the presence of electric and magnetic fields'', Am. J. Phys. '''73''', 293 (2005). [http://dx.doi.org/10.1119/1.1819934 [PDF]] | ||
== Lecture | == Lecture 8: Mean-field theories of phase transitions == | ||
* 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. | ||
| Line 77: | Line 74: | ||
* J. Als‐Nielsen and R. J. Birgeneau, ''Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions'', Am. J. Phys. '''45''', 554 (1977). [http://dx.doi.org/10.1119/1.11019 [PDF]] | * J. Als‐Nielsen and R. J. Birgeneau, ''Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions'', Am. J. Phys. '''45''', 554 (1977). [http://dx.doi.org/10.1119/1.11019 [PDF]] | ||
== Lecture | == Lecture 9: Renormalization group (RG)== | ||
* [[Media:rg_phys813.pdf|PDF]] | * [[Media:rg_phys813.pdf|PDF]] | ||
* Example: RG for 1D and 2D Ising model. | * Example: RG for 1D and 2D Ising model. | ||
| Line 91: | Line 88: | ||
== Lecture 11: Elements of nonequilibrium statistical physics: Boltzmann equation and Kubo formula == | == Lecture 11: Elements of nonequilibrium statistical physics: Boltzmann equation and Kubo formula == | ||
* [[Media:boltzmann_kubo.pdf|PDF]] | * [[Media:boltzmann_kubo.pdf|PDF]] | ||
===Additional references=== | ===Additional references=== | ||
* N. Borghini, [[Media:BOOK_BORGHINI=topics_in_nonequilibrium_physics.pdf|Topics in Nonequilibrium Physics]] | * N. Borghini, [[Media:BOOK_BORGHINI=topics_in_nonequilibrium_physics.pdf|Topics in Nonequilibrium Physics]] | ||
== Lecture 12: Elements of nonequilibrium statistical physics: Master equations for open quantum systems == | |||
* Example: Decoherence in quantum Brownian motion. | |||
* Example: Linblad master equation. | |||
* Example: Bloch equation describing spin relaxation and dephasing. | |||
=== 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). [http://dx.doi.org/10.1119/1.3043847 [PDF]] | |||
Revision as of 11:51, 23 February 2018
Lecture 1: Failure of classical statistical mechanics
Additional references
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 the quantum canonical ensemble.
- Example: Density matrix and quantum partition function for a linear harmonic oscillator in the quantum canonical ensemble.
Additional references
- Dirac notation and mathematical prerequisites for quantum mechanics (Chapter 1 from L. E. Ballentine: Quantum Mechanics - A modern development, second edition).
- A. Ekert and P. L. Knight, Entangled quantum systems and the Schmidt decomposition, Am. J. Phys. 63, 415 (1995). [PDF]
- Steven Weinberg, Quantum mechanics without state vectors, Phys. Rev. A 90, 042102 (2014). [PDF]
Lecture 3: Many-particle wave function and the Hilbert space of identical particles
- Example: Wave functions of 3 fermions and 3 bosons.
Lecture 4: Quantum partition function for many-particle systems in equilibrium
- 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.
- Quantum partition function for non-interacting 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 in equilibrium
- Example: Heat capacity of electrons in solids.
- Example: Pauli paramagnetism.
- Example: Landau diamagnetism.
- Example: Stoner ferromagnetism.
- Example: White dwarfs, neutron stars and black holes.
Additional references
- R. Balian and J.-P. Blaizot, Stars and statistical physics: A teaching experience, Am. J. Phys. 67, 1189 (1999). [PDF]
- Stelar evolution: The life and death of stars
Lecture 6: Degenerate bosons in equilibrium
- 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.
- Example: Magnons in the Heisenberg model of magnetism.
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 in magnetic systems
- Example: Noninteracting spins.
- Thermodynamics of magnetism.
- Abrupt vs. continuous phase transitions in ferromagnet-paramagnet systems and analogy with liquid-gas phase diagram.
- Example: Partition function of the Ising model in one-dimension in an external magnetic field.
- Example: Onsager exact analytical solution vs. 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]
Lecture 8: Mean-field theories of phase transitions
- Example: Mean-field theory of the Ising model of magnetism.
- Example: Mean-field theory of the XY model of magnetism.
- Landau phenomenological formulation of mean-field theories.
- Landau-Ginzburg mean-field theory and the Ginzburg criterion for the importance of fluctuations.
Additional references
- J. Als‐Nielsen and R. J. Birgeneau, Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions, Am. J. Phys. 45, 554 (1977). [PDF]
Lecture 9: Renormalization group (RG)
- 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]
Lecture 11: Elements of nonequilibrium statistical physics: Boltzmann equation and Kubo formula
Additional references
- N. Borghini, Topics in Nonequilibrium Physics
Lecture 12: Elements of nonequilibrium statistical physics: Master equations for open quantum systems
- Example: Decoherence in quantum Brownian motion.
- Example: Linblad master equation.
- Example: Bloch equation describing spin relaxation and dephasing.
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]
