Theoretical Statistical Physics
Course description
At Heidelberg, the course on statistical physics is a core course of the master studies program, although in practise it is attended also by many bachelor students. In the winter term 2022/23, it takes place every Tue and Thu at 11.15 am at HS2 in the physics lecture building Im Neuenheimer Feld 308 (and not at gHS at Philosophenweg 12 as announced initially). The lecture runs for 90 min and because the blackboard has to be cleaned from time to time, there will be ample time to relax or ask questions during the lecture. This lecture will not be streamed or recorded, except the Corona situation turned really bad again, so please plan to come to the lecture in person.
As you know from your introductory lectures, physics often focuses on simple systems that can be solved exactly, like the Kepler problem in classical mechanics or the hydrogen atom in quantum mechanics. More complex problems like the three-body problem or the hydrogen molecule quickly become untractable and require perturbation theory or numerical solutions. Interestingly, however, systems of many particles become more tractable again, because many microscopic properties are averaged out. For systems of many particles, it is neither possible nor desirable to follow all microscopic details, so a physical description has to be statistical in nature. In the limit of infinite system size, statistical physics actually gives the same formal structure as does thermodynamics, which is the most univeral and successful theory in physics (if you believe Einstein, but who does not). Like thermodynamics, statistical physics has many applications, in particular in solid state physics, atomic and molecular physics, biophysics, astrophysics and environmental physics, which all deal with complex systems with many components.
Because it officially is a master course, this lecture will be given in English (with a German accent). We will hand out weekly exercises and you have to successfully solve >50% to be admitted to the final exam in February. You are allowed to work in groups of two for the exercises and you are expected to attend the tutorials. We also will give some numerical exercises plus some bonus exercises over the Xmas break.
There are many different ways to approach statistical physics and this will also be explained in the lecture. This lecturer likes to start with a short recap of the mathematics of probability distributions. We then discuss the fundamental postulate of the microcanonical ensemble (all allowed states are equally likely) and continue to the canoncial and grandcanoncial ensembles, which are simply transformations to other variables. With this we already have derived thermodynamics. We then can start with ideal quantum systems such as Fermi and Bose fluids (which have no explicit interaction, but implicitly interact through their rules of counting). Next we go to interacting classical systems like the van der Waals fluid and the Ising model for lattice spins. This also allows us to introduce the concept of renormalization group theory. In the end we also will discuss some non-equilibrium physics, including stochastic equations and stochastic thermodynamics.
Recommended reading
There are many good textbooks and here is a small selection. First the usual suspects from series on theoretical physics:
- Thorsten Fliessbach, Statistische Physik, Lehrbuch zur Theoret. Physik IV, Spektrum 2018
- Wolfgang Nolting, Grundkurs Theoretische Physik 6, Statistische Physik, Springer 2013
- Landau-Lifshitz, Statistical Physics, volume 5 of the series on Theoretical Physics, Butterworth-Heinemann 1980
- The Feynman Lectures on Physics, Millennium Edition 2011
Then some classical books:
- Herbert Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition, John Wiley & Sons 1985
- David Chandler, Introduction to Modern Statistical Mechanics, Oxford Univ Pr 1987
- Kerson Huang, Statstical Mechanics, 2nd edition, John Wiley & Sons 1987
- Frederick Reif, Fundamentals of Statistical and Thermal Physics, Macgraw-Hill 1965
Finally some modern textbooks:
- Franz Schwabl, Statistische Mechanik, 3. Auflage, Springer 2006
- Josef Honerkamp, Statistical Physics, 2nd edition, Springer 2002
- James Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford Master Series in Physics 2006
- Luca Peliti, Statistical Mechanics in a Nutshell, Princeton University Press 2011
- Luca Peliti and Simone Pigolotti, Stochastic Thermodynamics, Princeton University Press 2021
Material
- Intro slides from the first lecture:
- Introduction_2022_10_18.pdf
- Script from winter term 2020/21
- ScriptStatPhys2020.pdf
- Presence sheet, discussed in first tutorial:
- TheorStatPhys_WS22_Presence.pdf
- Current version of script
- TheorStatPhys_WiSe2223_TrialExam.pdf
- PhaseDiagrams.pdf
- FinalPresentation_2023_02_09.pdf
- Roomplan for the first exam:
- roomplan2223.pdf
- Final version script
- ScriptStatPhys_2023_02_24.pdf
- Room plan second exam
- roomplan2223_NK.pdf
Exercise sheets
- sheet 1
- sheet 2
- sheet 3
- sheet 4
- sheet 5
- sheet 6
- sheet 7
- sheet 8
- sheet 9
- sheet 10
- sheet 11
- sheet 12 (Bonus)
Practice groups
- Group 01 (Jenna Elliott)
18 participants
Philos.-weg 12 / R 058, Thu 14:15 - 16:00 - Group 02 (Jonas Wessely)
18 participants
Philos.-weg 12 / R 060, Thu 14:15 - 16:00 - Group 03 (Simon Brauburger)
19 participants
Philos.-weg 12 / R 059, Fri 9:15 - 11:00 - Group 04 (Falko Ziebert)
20 participants
Philso.-weg 12 / R 060, Fri 9:15 - 11:00 - Group 05 (Serena Giardino)
17 participants
Philos.weg 12 / R 056, Fri 11:15 - 13:00 - Group 06 (Dennis Wörthmüller)
16 participants
Philos.-weg 12 / R 058, Fri 11:15 - 13:00 - Group 07 (Marc Bauer)
18 participants
Phil.-weg 12 / R 070, Fri 11:15 - 13:00 - Group 08 (Shaun Fell)
14 participants
Philos.-weg 12 / kHS, Fri 14:15 - 16:00 - Group 09 (Johannes Blumberg)
20 participants
INF 227 / HS 2, Fri 14:15 - 16:00 - Group 10 (Keisuke Fujii)
14 participants
Philos.-weg 12 / R 105, Fri 14:15 - 16:00 - Group 11 (Michael Heinrich)
18 participants
Philos.-weg 12 / R 060, Fri 14:15 - 16:00 - Group 12 (Rabea Link)
21 participants
INF 227 / SR 2.404, Fri 14:15 - 16:00 - Group 13 (Federica Capellino)
18 participants
INF 227 / SR 3.403, Fri 14:15 - 16:00 - Group 14 (inactive)
22 participants