## Wintersemester 2018-2019

### Classical Complex Systems

**Prof. G. Stock, Dr. S. Wolf**

**Lecture in Advanced Theoretical Physics (9 CP)**

**4 SWS: **Monday, 10-12, Tuesday 12 - 14, SR GMH

**1. Lecture:** Monday, 15.10.2018

**Exercises (Computer Lab): Dr. S. Wolf**

**
Organization**

**Materials**

**Registration for computer exercises**

**Synopsis:** Recent advances in theoretical and computational sciences have made it possible to achieve a "first principles" description of complex phenomena, such as the dynamical properties of materials and the functional motion of biomolecules. To this end, the lecture aims to provide an introduction into basic computational strategies (such as molecular dynamics and Monte-Carlo simulations) as well as powerful statistical theories (such as Langevin and Master Equations). The lessons are accompanied by computer exercises, which provide an hands-on experience of the topics.

**Preliminary Program**

I. Introduction

II. Simulation Approach

- First Principles Description
- Probability Distributions and Sampling
- Molecular Dynamics and Monte-Carlo Simulations
- Description of Time-dependent Phenomena

III. Theory of Open Systems

- Langevin Equations
- Fluctuation-Dissipation Theorem
- Fokker-Planck Equations
- Transition State Theory
- Theory of Stochastic Processes
- Master Equations

IV. Nonlinear Dynamics

- Theory of Deterministic Chaos
- Nonlinear Models

**Literature:**

- H.J.C. Berendsen:
*Simulating the Physical World* - D. Frenkel, B. Smit:
*Understanding Molecular Simulation* - R. Zwanzig:
*Nonequilibrium Statistical Mechanics* - N.G. van Kampen:
*Stochastic processes in Physics and Chemistry* - R.H. Landau, M.J. Páez, C.C.Bordeianu:
*Computational Physics (3rd edition)* - A. Nitzan:
*Chemical Dynamics in Condensed Physics*