Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title STATISTICAL PHYSICS
Code MATH327
Coordinator Dr DA Schaich
Mathematical Sciences
David.Schaich@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2022-23 Level 6 FHEQ Second Semester 15

Aims

1. To develop an understanding of the foundations of Statistical Physics normally including statistical ensembles and related extensive and intrinsic quantities.
2. To develop an understanding of the properties of classical and quantum gases and an appreciation of their applications to concepts such as the classical equation of state or the statistical
theory of photons.
3. To obtain a reasonable level of skill in using numerical computer programming to describe diffusion and transport in terms of stochastic processes.
4. To know the laws of thermodynamics and thermodynamical cycles.
5. To obtain a reasonable understanding of interacting statistical systems and related phenomenons such as phase transitions.

Learning Outcomes

(LO1) Demonstrate understanding of the microcanonical, canonical and grand canonical ensembles, their relation and the derived concepts of entropy, temperature and particle number
density.

(LO2) Understand the derivation of the equation-of-state for non-interacting classical or quantum gases.

(LO3) Demonstrate numerical skills to understand diffusion from an underlying stochastic process.

(LO4) Know the laws of thermodynamics and demonstrate their application to thermodynamic cycles.

(LO5) Be aware of the effect of interactions including an understanding of the origin of phase transitions.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

(S4) Communication skills

(S5) IT skills

(S6) Organisational skills

(S7) Teamwork

Syllabus
 

1. The central limit theorem
2. The microcanonical ensemble and the definition of temperature
3. Derivation of the canonical ensemble
4. Particle number, grand-canonical ensemble and the chemical potential.
5. Classical gases and the equipartition theorem.
6. The classical equation of state.
7. Quantum gases: blackbody radiation and Fermi gases.
8. The 1-dimensional chain and the phonon dispersion relation.
9. From Brownian motion to the diffusion equation
10. Anomalous diffusion: a computer experiment
11. Van der Waals equation of state and the liquid gas phase transition
12. Critical phenomena
13. The Ising model in 1 dimension
14. Peierls argument of a phase transition in 2 dimensions
15. The 2-d Ising model in mean field approximation and critical phenomena

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment  120    55       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 2  0    15       
Homework 1  0    15       
Computer-based homework project  0    15