Statistical and Thermal Physics, II, 7.5 credits

Entry requirements

Entry requirement for studies on third-cycle education courses

• second-cycle degree,
• 240 credits in required courses, including at least 60 second-cycle credits, or
• acquisition of equivalent knowledge in some other manner

Specific entry requirements for this course (if applicable)

Knowledge of statistical mehcanis and thermodynamics at the level of the first course 6FIFM46 Statistical and Thermal Physics, I”. Quantum Mechanics,

Learning outcomes

By the end of the course the students will be able to:

• Understand and solve problems in select topics in statistical mechanics, as given by the Part 1 course contents.
• Understand how the statistical mechanics underpinnings of atomistic simulation methods, including molecular dynamics and monte carlo methods, and apply this knowledge in actual simulations

Contents

After an initial recap of the basics of equilibrium statistical mechanics and thermodynamics, the course contains two parts:

Part 1: Select topics in statistical mechanics:

• Quantum statistical mechanics: density-matrix formalism and quantum ensembles;
• Equilibirum fluctuations and response
• Correlation functions.
• Linear-response, Green–Kubo relations and transport coefficients
• Stochastic dynamics: Langevin dynamics, fluctuation–dissipation relations, the Fokker–Planck equation
• Phase transitions: order parameters and Landau theory, intro to critical phenomena.

Part 2: Applications of statistical mechanics in atomistic simulation:

• Molecular dynamics: equations of motion, time averages, ensemble averages, ergodicity, integration algorithms, conservation laws
• Ensembles in molecular dynamics: thermostats, barostats
• Monte Carlo methods: Importance sampling, the Metropolis algorithm,
• Statistical analysis of simulation data: equilibration, autocorrelation times, uncertainty estimates
• Free-energy methods: phonons, thermodynamic integration, free-energy perturbation etc
• Rare events and enhanced sampling methods.

Educational methods

The course will consist of a set of lectures and tentatively one or more computer lab excersises.

Examination

The course will be examined through a set of hand in assignments and an oral exam.

Grading

Course literature

• Tuckerman, Mark E. Statistical Mechanics: Theory and Molecular Simulation. Second edition. Oxford University Press, 2023, ISBN: 978-0-19-882556-2.
• Select handouts/lecture notes.