Ruprecht Karls Universität Heidelberg

Theoretical Statistical Physics Winter Term 2017/18

Attention: the lecture has been shifted to INF 308, HS2 !!!

Introduction

Statistical physics deals with the properties of physical systems with many particles. For macroscopic systems like gases, liquids and solids, we know today that they typically contain 6x10^23 particles (Avogadro number). For systems with that many particles, it is neither possible nor desirable to follow all the details of the microscopic dynamics, irrespective of whether the system of interest is of classical or quantum nature. A reasonable description of many-particle-systems therefore has to be a statistical one. This lecture provides an introduction to the fundamentals and main applications of statistical physics for first-year master students. It can also be attended by interested bachelor students who have completed the four introductory courses in theoretical physics. In contrast to other fundamental fields of theoretical physics, such as mechanics or electrodynamics, there is still a lot of current research in statistical physics, for example in regard to non-equilibrium statistical physics or complex systems. Some examples of on-going research will be included in this course. Statistical physics is everywhere and examples for application areas are condensed matter physics, astrophysics and biophysics.

Being part of the master studies, the lectures will be given in English. There are two lectures each week, on Tuesday and Thursday from 11.15-12.45 (no break) in the large lecture hall at Philosophenweg 12. The exercises will be organized by Falko Ziebert and registration occurs as usual through the webpages of the department of physics and astronomy. Each week there is a new sheet of exercises provided through the web and solutions have to be handed in one week later. Students are allowed to work together in groups of up to two. In order to be allowed to the final exam, you have to solve successfully more than half of the exercises. Some exercises will involve computer programming on an elementary level. A script is available from an earlier version of this course (winter term 2015/16) and will be improved during this one.

Content

  1. Probability theory: random variables, probability distributions, moments, central limit theorem, random walks, information entropy (Shannon), mutual information, principle of maximal entropy (Jaynes), conditional probabilities, Bayes' theorem
  2. Equilibrium ensembles: microcanonical, canonical and grandcanonical ensembles, ideal gas, thermodynamic potentials, Legendre transformations, Maxwell relations, material properties, thermodynamic engines, work and heat, chemical reactions
  3. Ideal quantum systems: Fermi gas, Bose gas, photons, Stefan-Boltzmann law, Planck radiation formula, Bose-Einstein condensation, phonons, specific heat of solids, Einstein model, Debye model
  4. Classical fluids: real gases, virial expansion, van der Waals-fluid, Maxwell-construction, phase diagrams, critical phenomena
  5. Magnetic systems: lattice gases, 1D and 2D Ising model, Peierls argument for phase transition, Onsager solution
  6. Numerical methods: molecular dynamics, thermostat, importance sampling, Monte Carlo methods, Metropolis algorithm
  7. Dynamics and non-equilibrium physics: Brownian motion, random walks, Fokker-Planck equation, Langevin equation, fluctuation-dissipation theorem

Material for the course (access restricted to UHD)

The usual suspects

  • Thorsten Fliessbach, Statistische Physik, Lehrbuch zur Theoret. Physik IV, Spektrum
  • Wolfgang Nolting, Grundkurs Theoretische Physik 6, Statistische Physik, Springer

Other up-do-date textbooks

  • Franz Schwabl, Statistische Mechanik, 3. Auflage, Springer 2006
  • Josef Honerkamp, Statistical Physics, 2nd edition, Springer 2002
  • Luca Peliti, Statistical Mechanics in a Nutshell, Princeton University Press 2011
  • James Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford Master Series in Physics 2006

Classical textbooks

  • Landau-Lifshitz volume 5
  • Frederick Reif, Fundamentals of Statistical and Thermal Physics, Macgraw-Hill 1965
  • Herbert Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition, John Wiley & Sons 1985
  • Kerson Huang, Statstical Mechanics, 2nd edition, John Wiley & Sons 1987
  • Terrell L. Hill, An Introduction to Statistical Thermodynamics, Dover 1960
  • Donald McQuarrie, Statistical mechanics, Univ Science Books 2000
  • David Chandler, Introduction to Modern Statistical Mechanics, Oxford Univ Pr 1987

Scripts by local lecturers

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