Statistical physics, Phys504b/AM531. Winter/spring 2008
Statistical physics provides the microscopic foundations, based on particles, fields and their interactions, of thermodynamics. Importantly, statistical mechanics is THE systematic framework to study real-world problems consisting of complex interactions. Examples run from molecular modeling to chaos, protein interaction networks, gene regulation, social dynamics, behavior of large populations and to stock trading, to mention some. Besides providing the tools, statistical physics provides the intellectual framework to study very diverse problems.See also:
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Movie: StatMech is also fun!: Jacob Alldredge's This Is Stat Mech (from Jim Sethna's pages).
Movie: Statistical Physics, Computer Simulation, and Probability
New Scientist article: Statistical physics predicts stock market gloom
Rough (tentative) outline
- Review of thermodynamics
- Thermodynamic potentials
- Basic concepts of probability
- Distribution functions
- Liouville's theorem
- Ideal gases
- Real gases. Virial expansion. Cluster expansion.
- Liquids. BBGY hierarchy.
- Quantum liquids and solids.
- Ising model.
- Phase transitions.
- Mean field theory
- Computational matters.
- Applications.
Lecturer:
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Dr. Mikko Karttunen. Email: mkarttu [at] uwo.ca.
IMPORTANT: When emailing, please include 'PHYS504b/AM531' on the subject line.
Material:
- Statistical Mechanics - From First Principles to Macroscopic Pheomena by J. Woods Halley (Cambridge, 2007). The book is available at the university book store.
- Lecture notes.
Lectures (check for changes!):
- Tuesdays: 10:30-11:30
in Physics 106.
Tuesdays' lectures will in MC15B. - Thursdays: 8:30-10:30 in the physics board room.
- First lecture:
Tuesday Jan. 8, 2008.
due to scheduling conflicts, we start on Tuesday Jan 15, 2008. - Thu Jan 17: Review of the basic concepts in thermodynamics. Book: Part I, Ch 3, pp. 37-4
- Tue Jan 22: Mathematical tools: Exact differentials, Jacobians
- Thu Jan 24: Legendre transforms, equations of state (ideal gas, van der Waals, virial expansion), introduction to pair correlations & interactions
- Tue Jan 29: Laws of thermodynamics
- Thu Jan 31: Free energies
- Tue Feb 5: Quiz 1
- Thu Feb 7: Response functions. Fundamental concepts in statistical mechanics: Phase space
- Tue Feb 12: Phase space, Poisson brackets
- Tue Feb 14: Probability: Permutations and combinations, probability distributions
- Tue Feb 19: Moments and characteristic functions, some important distributions
- Tue Feb 21: Liouville equation.
- Feb. 25-29: Reading week. No classes
- Tue. Mar. 4: Mean field theory
- Thu. Mar. 8: The Ising model, introduction to the Landau theory of phase transitions. The importance of symmetery & order parameter.
- Special topics: Superconductivity, XY-model, topolgical defects
- Detailed derivations of the Microcanonical ensemble
- Detailed derivations of the Canonical ensemble
- Quantum statistics
- Introduction to (Metropolis) Monte Carlo
Assessment and exam dates:
- The best of the two following options:
- two quizzes (each worth 25%) & final exam (50%)
- final exam 100%
- Exam Dates:
- Quizz 1: Tue, Feb. 5
-
Covers assignments 1 & 2 and all the lecture material up to Thu Jan. 31.
- Quizz 2: Tue, Mar. 11
- Final: Tue, Apr. 15 at 1-4 pm. Room: MC 15B.
- Quizz 1: Tue, Feb. 5
- Assignments will not be marked BUT the Quizzes will be heavily based on them.
Other important dates
- Reading week: Feb 25-29
- APS March Meeting: Mar 10-14
Some suggestions for additional reading:
- L.E. Reichl: A Modern Course in Statistical Physics
- K. Huang: Statistical Mechanics
- R.K. Pathria: Statistical Mechanics
On the net:
- Thermal and Statistical Physics by Harvey Gould and Jan Jan Tobochnik (Clark Univ.).
- Statistical Mechanics: Entropy, Order Parameters, and Complexity by Jim Sethna (Cornell).
- Statistical Mechanics by Mark Tuckerman (NYU)
Academic integrity:
-
Working together is encouraged. Copying, plagiarism and cheating of
any kind is absolutely forbidden.
On-line material & problem sets for winter/spring 2008
- Lecture notes:
- Central limit theorem in a nutshell (2 files): 1, 2
- Ising model & intro to Landau theory 1.
- Landau theory & symmetry
- Notes on superconductivity, XY-model & topological defects
- Problem sets: the first one will be posted on Thu. Jan 24.