##
Topics in Nonequilibrium Statistical Mechanics

Lectures by Martin Howard and
Kent Baekgaard Lauritsen

Thursdays **13:15 - 15:00** in **Kc7 **

Course start: February 5, 1998.

**Contents:**

- Introduction
- Random walk:

Langevin equation, Fokker-Planck equation, Fluctuation dissipation
theorem, Master equation, Detailed balance
- Interfaces:

Scaling, Symmetries, Noise, Edwards-Wilkinson equation,
Kardar-Parisi-Zhang (KPZ) equation, Renormalization group (RG) analysis,
Burgers equation, Driven diffusive systems (DDS), Directed Polymers,
Noisy Kuramoto-Sivashinsky equation, Master equation,
Pinning/depinning transitions, Quenched noise
- Directed percolation (DP):
Models, Langevin description, Absorbing state, Multiplicative noise,
Nonequilibrium phase transition, Critical exponents,
Reggeon field theory, Renormalization group results,
Reaction diffusion systems, Master equation,
Branching and annihilating random walks,
Surface critical behaviour
- Phase ordering, Conserved and nonconserved order parameters,
Persistence exponents
- Self-organized criticality (SOC):
Sandpile models, Avalanches, Critical exponents,
Mean-field theory, Self-organized branching processes,
Order parameter, External drive, Field-theoretic approach
- Advanced topics:
Martin-Siggia-Rose field-theory formalism
RG: calculation of fixed points and exponents

**Literature:**

- Intro: J. M. Yeomans, Statistical mechanics of phase transitions,
Oxford science publications, 1992, chapters 1-4, 8 (85 pp).
J. Cardy, Scaling and renormalization in statistical physics,
Cambridge University Press, 1996: chapters 1-2 (20pp).
- KPZ: A.-L. Barabasi and H. E. Stanley, Fractal concepts in surface growth,
Cambridge university press 1995, chapters 1-11, 26 (135 pp).
- DP: R. Dickman, in Nonequilibrium statistical mechanics in one dimension,
ed. V. Privman, Cambridge press, 1996.
J. Cardy, Scaling and renormalization in statistical physics,
Cambridge University Press, 1996: chapter 10.
- SOC: G. Grinstein, in Scale invariance, interfaces and nonequilibrium
dynamics, ed. A. McKane et al., NATO advanced study institute series B:
physics vol. 344, Plenum, New York, 1995.
Articles, notes.

**Exam:** Take home exam(s)

**Points:** 2 or 4