PHYC40650 Advanced Statistical Physics

Academic Year 2021/2022

The course covers several themes from fundamental research where statistical physics plays the central role:
1. Phase transitions
2. Polymer mechanics
3. Plasmas and electrolytes
4. Stochastic and non-equilibrium processes
Through theoretical description of these phenomena, the students will learn how to construct and use physical models as a mean for the qualitative and quantitative explanation and understanding of phenomena and processes in Nature. The models will be solved using several essential analytical techniques in theoretical physics including mean field theory, variational principle, transfer matrix method, renormalisation group theory, lattice models, classical field theory, Green's functions, etc.

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Curricular information is subject to change

Learning Outcomes:

On completion of this module students should:
1. Have understood the meaning of the partition function and how to use it for calculation of thermodynamic properties of condensed matter systems;
2. Have understood the concept of statistical ensemble;
3. Be familiar with the concept of a phase transition and critical behaviour and be able to describe the signatures of a phase transition;
4. Have understood the concept of fluctuations and describe their effect on thermodynamic quantities;
5. Be able to describe the geometry and elasticity of a polymer chain;
6. Be able to recognise the signatures of entropic forces and calculate their magnitude in molecular systems;
7. Be able to do basic calculations using the lattice models in condensed matter;
8. Be familiar with the ways of describing non-equilibrium processes in condensed matter and biophysics.

Indicative Module Content:

1. Phase transitions: Landau theory, critical fluctuations, scaling, renormalisation group method
2. Lattice models: transfer matrix method, exact solution of the Ising model, mean field theory
3. Polymers: statistics of an ideal chain, Gaussian chain, self-avoiding chain, worm-like chain
4. Entropic forces at the nanoscale: depletion interactions, entropic springs, polymer chain elasticity
5. Charged systems: Poisson-Boltzmann equation in planar, cylindrical and spherical geometry, charge binding, charge correlations, Wigner crystals, strong coupling theory
6. Diffusion and Brownian motion: Langevin equation, Gaussian random walk, Levy flights.
7. Non-equilibrium processes: Kramers problem, active particles

Student Effort Hours: 
Student Effort Type Hours
Lectures

30

Tutorial

6

Autonomous Student Learning

75

Total

111

Approaches to Teaching and Learning:
- 100% blackboard module
- 6 tutorials with interactive problem solving
- online notes available 
Requirements, Exclusions and Recommendations
Learning Recommendations:

PHYC30010 - Thermodynamics and Statistical Mechanics


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: End of Term 2 hour End of Trimester Exam No Graded No

50

Assignment: Problem sheets Throughout the Trimester n/a Graded No

50


Carry forward of passed components
No
 
Resit In Terminal Exam
Summer Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment
• Feedback individually to students, post-assessment

How will my Feedback be Delivered?

- graded assignments, returned to students with comments - exam feedback upon request

1. Landau, Lifshitz. Vol. 5. Statistical physics part 1
2. Baxter, Exactly Solved Models in Statistical Mechanics
3. McQuarrie. Statistical Mechanics
4. Chandler, Introduction to modern statistical mechanics
5. Teraoka, Polymer Solutions: An Introduction to Physical Properties
Name Role
Dr Konstantinos Kotsis Lecturer / Co-Lecturer
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Spring
     
Lecture Offering 1 Week(s) - 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32 Fri 09:00 - 09:50
Lecture Offering 1 Week(s) - 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32 Fri 13:00 - 13:50
Lecture Offering 1 Week(s) - 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32 Mon 13:00 - 13:50
Spring