## Wintersemester 2017-2018

### Classical Complex Systems

**Prof. G. Stock**

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

**4 SWS: **Monday, 10-12, Wednesday 14 - 16, SR GMH

**Exercises (Computer Lab): Dr. Steffen Wolff**

**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.

**Organization**

**Materials**

Registration for computer exercises

**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*

## Term Paper: Stochastic Dynamics

**Lecturers: Prof. Dr. Tanja Schilling, Prof. Dr. Gerhard Stock**

**Summary: **Topics include Random Walks, Theorem by Bochner, Khinchin and Wiener, Brownian motion, Langevin Equations, Transition State Theory, Ratchets Monte Carlo and Molecular Dynamics Methods.

Materials

**List of presentations:**

- 14.11.2017

Moritz, Topic: Brownian Motion

- 21.11.2017

entfällt

- 28.11.2017

entfällt

- 05.12.2017

Adrian, Topic: Levy Flight

- 12.12.2017

Jan, Topic: Markov Models

- 09.01.2018

Yasmin, Topic: Energy Landscapes

- 16.01.2018

Neil, Topic: Kramers Theory

- 23.01.2018

Philip, Topic: Maximum Caliber

- still slots available!