### Instruction

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Kinetic Theory | 10 Cr | General Examination | 17.4.2020 - 17.4.2020 | ||

Kinetic Theory | 10 Cr | General Examination | 5.6.2020 - 5.6.2020 |

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Kinetic Theory | 10 Cr | General Examination | 13.12.2019 - 13.12.2019 | ||

Kinetic Theory | 10 Cr | Lecture Course | 3.9.2019 - 12.12.2019 | ||

Kinetic Theory | 10 Cr | General Examination | 24.8.2018 - 24.8.2018 | ||

Kinetic Theory | 10 Cr | General Examination | 15.6.2018 - 15.6.2018 | ||

Kinetic Theory | 10 Cr | Lecture Course | 15.1.2018 - 4.5.2018 |

### Target group

Masterâ€™s Programme in Theoretical and Computational Methods is responsible for the course.

Module where the course belongs to:

**TCM300 Advanced Studies in Theoretical and Computational Methods**

The course is available to students from other degree programmes.

### Prerequisites

Candidate level courses Vuorovaikutukset ja Aine, Fysiikan Matemaattisen MenetelmÃ¤t IIb, Termofysiikan perusteet, Statistinen mekaaniikka, or equivalent knowledge of mathematical methods, Newtonian dynamics, basic thermodynamics and statistical mechanics of particles.

### Learning outcomes

The main goal of the course is to present an overview of kinetic theory, of its foundations, properties and applications. After the course, the student will be able to identify a number of physical systems whose transport properties can be studied using a Boltzmann transport equation, and will know how the solutions of the equation are connected to the evolution of the microscopic system. The most important generic features of solutions of Boltzmann equations are presented, and we learn how these properties can be used for computing non-equilibrium transport properties of the system, such as values of transport coefficients.

### Timing

The course will not be offered every year and its teaching periods might also vary.

### Contents

The course provides an overview of kinetic theory and of its main uses in studying transport of particles and energy in a wide variety of physical systems. One important example is the kinetic theory of a rarefied gas of classical particles with short-range interactions. In the Boltzmann-Grad scaling limit, the state of this system can be determined by solving a Boltzmann transport equation. We get acquainted with its main properties and uses: the H-theorem and how it is related to increase of entropy, how equilibrium states can be solved from an entropy production functional, and how the linearized Boltzmann equation is connected to computation of non-equilibrium transport coefficients via the Green-Kubo formula. We discuss the closely connected relaxation time approximation. In the second part, we present further examples of physical systems (for example, wave transport in random media and transport by phonons in crystalline structures) whose transport properties can be studied via similar Boltzmann equations. If time permits, we can also briefly discuss the Boltzmann-Nordheim (aka Uehling-Uhlenbeck) transport equations for weakly interacting quantum fluids. Another optional topic is how diffusive and superdiffusive transport can arise from solutions of inhomogeneous Boltzmann equations.

### Study materials

Course lecture notes

### Recommended optional studies

Stochastic methods or equivalent studies about basics of probability theory.

### Completion methods

The course is completed either with sufficient amount of exercise and course exam problems, or alternatively by a final exam if agreed in advance with the lecturer.