QHE

Statistical Physics

Text:

L.E.Reichl, "A Modern Course in Statistical Physics", 2nd ed., Wiley, 1998.

Revised Mathematical Supplement


Chapter 5: Stochastic Dynamics and Brownian Motion

  •    5.A. Introduction       ( Oct 25, 2017 )
  •    5.B. General Theory       ( Aug 12, 2018 )
  •    5.C. Markov Chains       ( May 26, 2018 )
  •    5.C.1. Spectral Properties       ( May 26, 2018 )
  •    5.C.2. Random Walk       ( May 22, 2018 )
  •     5.D. The Master Equation
  •    5.D.1. Derivation of the Master Equation       ( May 23, 2018 )
  •    5.D.2. Detailed Balance       ( May 23, 2018 )
  •    5.D.3. Mean First Passage Time       ( May 24, 2018 )
  •     5.E. Brownian Motion
  •    5.E.1. Langevin Equation       ( Nov 23, 2017 )
  •    5.E.2. The Spectral Density       ( May 24, 2018 )
  •    Zip file for Chap.5       ( Aug 12, 2018 )

    Special Topics

  •    S5.A. Time Periodic Markov Chain       ( Jun 04, 2018 )
  •     S5.B. Master Equation for Birth-Death Processes
  •    S5.B.1. The Master Equation       ( Jun 04, 2018 )
  •    S5.B.2. Linear Birth-Death Processes       ( Jun 02, 2018 )
  •    S5.B.3. Nonlinear Birth-Death Processes       ( Jun 03, 2018 )
  •     S5.C. The Fokker-Planck Equation
  •    S5.C.1. Probability Flow in Phase Space       ( Jun 04, 2018 )
  •    S5.C.2. Probability Flow for Brownian Particle       ( Jun 04, 2018 )
  •    S5.C.3. The Strong Friction Limit       ( Jun 03, 2018 )
  •    S5.C.4. Solution of Fokker-Planck Equations with One Variable       ( Jun 03, 2018 )
  •    S5.D. Approximations to the Master Equation       ( Jun 03, 2018 )
  •    Zip file for Special Topics       ( Jun 04, 2018 )

    Chapter 6: The Foundations of Statistical Mechanics

  •    6.B. The Classical Probability Density       ( Jun 05, 2018 )
  •    6.C. Ergodic Theory and the Foundations of Statistical Mechanics       ( Dec 20, 2017 )
  •    6.C.1. Examples       ( Jun 28, 2018 )
  •    6.D. The Quantum Probability Density Operator       ( Dec 27, 2017 )
  •    Zip file for Chap.6 (contains 'TwoBallsOnBoundedPlane.nb')       ( Jun 28, 2018 )

    Special Topics

  •    S6.A. Reduced Probability Densities and the BBGKY Hierarchy       ( Dec 29, 2017 )
  •    S6.B. Reduced Density Matrices and the Wigner Distribution       ( Jan 08, 2018 )
  •    S6.C. Microscopic Balance Equations       ( Jan 26, 2018 )
  •    S6.D. Mixing Flow       ( Jan 29, 2018 )
  •    S6.E. Anharmonic Oscillator Systems       ( Feb 27, 2018 )
  •    Zip file for Special Topics (contains 'WalkerFord.nb')       ( Feb 27, 2018 )

    Chapter 8: Order-Disorder Transitions and Renormalization Group

  •    8.B. Static Correlation Functions & Response Functions       ( Mar 01, 2018 )
  •    8.C. Scaling       ( Mar 09, 2018 )
  •    8.D. Microscopic Calculation of Critical Exponents       ( Apr 10, 2018 )
  •    Zip file for Chap.8 (contains 'block.nb')       ( Apr 10, 2018 )

    Special Topics

  •    S8.A. Critical Exponents for the S4 Model       ( Apr 30, 2018 )
  •    S8.A.1. Contributions from the Second Cumulant       ( Apr 30, 2018 )
  •    Zip file for Special Topics (contains 'graphs.nb')       ( Apr 30, 2018 )

    Chapter 9: Interacting Fluids

  •    9.B. Thermodynamics and the Radial Distribution Function       ( Apr 12, 2018 )
  •     9.C. Virial Expansion of the Equation of State
  •    9.C.1. Virial Expansion and Cluster Functions       ( May 01, 2018 )
  •    9.C.2. The Second Virial Coefficient       ( May 02, 2018 )
  •    9.C.3. Higher Order Virial Coefficients       ( May 03, 2018 )
  •    Zip file for Chap.9 (contains '9.C.*_Code.nb')       ( May 03, 2018 )

    Special Topics

  •    S9.A. The Pressure and Compressibility Equations       ( May 04, 2018 )
  •    S9.B. Ornstein-Zernicke Equation       ( May 12, 2018 )
  •    S9.C. Third Virial Coefficient       ( May 13, 2018 )
  •    S9.D. Virial Coefficients for Quantum Gases       ( May 18, 2018 )
  •    Zip file for Special Topics       ( May 18, 2018 )

    Chapter 10: Hydrodynamic Processes Near Equilibrium

        10.B. Navier-Stokes Hydrodynamic Equations
  •    10.B.1. Balance Equations       ( Jul 07, 2018 )
  •    Appendix A. Balance Equations       ( May 27, 2018 )
  •    10.B.2. Entropy Source & Entropy Current       ( Jul 08, 2018 )
  •    10.B.3. Transport Coefficients       ( Jul 11, 2018 )
  •     10.C. Linearized Hydrodynamic Equations
  •    10.C.1. Linearization of the Hydrodynamic Equations       ( Jul 15, 2018 )
  •    10.C.2. Transverse Hydrodynamic Modes       ( Jul 15, 2018 )
  •    10.C.3. Longitudinal Hydrodynamic Modes       ( Jul 16, 2018 )
  •     10.D. Dynamic Equilibrium Fluctuations & Transport Processes
  •    Time Reversal Symmetry       ( Aug 06, 2018 )
  •    10.D.1. Onsagers Relations       ( Aug 13, 2018 )

  • Older version & notes for other chapters can be found      here


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