Course may be given in English.

Course will be given in period 4, spring 2001 if there is sufficient
interest.

First lecture, Monday 12 March, 10-12, Q12.

Lecturer: Clas Blomberg, Theoretical Physics, phone. 08-790 7176; email cob@theophys.kth.se

Brownian motion. Stochastic equations: The Langevin-equation, Master equations, Fokker-Planck-equations. Time series analysis. Wiener-Khinchin's theorem. Fluxes and forces, linear relations. The fluctuation-dissipation theorem. Irreversible thermodynamics.

Fluctuations i nonlinear systems with corresponding problems.

Exercises (as PostScriptfiles): Exercise1

F. Reif, Fundamentals of statistical and thermal physics, McGrawHill,
1965, chapter 13-15

K. Huang, Statistical Mechanics, John Wiley Paperback, 1987.

N G van Kampen: Stochastic Processes in Physics and Chemistry, North
Holland, paperback 1992

(A more extensive presentation of reference litterature will be given at
the lectures).

TENTATIVE SCHEDULE FOR THE SECOND PART (spring 2000):

6. Th 30/3 Stochastic description introduction. Examples of physical stochastic processes. Brownian Motion. Liouville Equation. (Lect. Notes 6.)

7. Mo 3/4 Basic features of stochastic processes. Markov processes. Master equations. Examples. (Lect. Notes 7)

8. Th 6/4 Examples, continuation. Methods for solving Master equations.
Random walk.

Time series analysis. Spectral analysis. Characterization of
noise. (Finish lect. notes 7, lecture notes 8).

9. Mo 10/4 Equations for stochastic processes. The Fokker-Planck
equation. Solutions. Brownian motion again. (Lect. Notes 9)

10. Th 13/4 Linear Response. The Fluctuation - Dissipation Theorem.
Start non-linear effects. (Lect. Notes 9, finish, 10)

EASTER INTERRUPTION

11. Mo 8/5 Linear response principles revisited. The basics of irreversible thermodynamics. Onsager relations. Entropy production and entropy flows. Principle of minimum entropy production. (Lect. Notes 11)

12. Th 11/5 Non-Equilibrium Thermodynamics, continuation. Non-linear effects. (Lect. Notes 12, continuation 10).

13. Mo 15/5 Summing up. Actual problems concerning fluctuations
and non-linear effects. (Lect. Notes 10 end, extra material).

Home exercises are given every Thursday. They are to be made before a date which will be determined during the course, 2-3 weeks after the course is finished.

For being approved as graduate student course or grade 5 as 'civilingenjörskurs', you shall try all exercises (you may avoid the most difficult ones), and most (but not necessarily everything) shall be correct.

For grade 3, you should have a little more than half of the exercises
correct, an you need not have solutions to all. For grade 4, more shall
be correct, but you need not try all exercises.