Undergraduate Course: Statistical Physics (PHYS11024)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Year 4 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  This is a course on the statistical physics of interacting particles. We begin by reviewing the fundamental assumptions of equilibrium statistical mechanics focussing on the relation between missing information (or entropy) and probability. We then consider the statistical mechanics of interacting particles and develop important approximation schemes. This leads us to review phase transitions and the unifying phenomenology. We study in detail a simple, microscopic model for phase transitions: the Ising model. We then consider a general theoretical framework known as
Landau Theory. Finally we discuss the issue of dynamics: how does a system approach and explore the state of thermal equilibrium? How does one reconcile microscopic time reversibility with the macroscopic arrow of time?

Course description 
I Derivation of Statistical Ensembles
 Maximising the missing information or Gibbs entropy
 Derivation of the principal ensembles: microcanonical; canonical; grand canonical
 Quantum systems: FermiDirac, BoseEinstein, classical limit
 BoseEinstein Condensation
II The ManyBody Problem
 Interacting systems
 Phonons and the Debye theory of specific heat of solids
 Perturbation theory and cluster expansion
 Breakdown of perturbation theory
 Nonperturbative ideas: DebyeH\"uckel Theory
III Transitions
 Phenomenology of phase transitions
 The Ising Model
 Solution in one dimension
 Correlation functions and correlation length
 Meanfield theory
 long range order in two dimensions, lack of in one dimension
 Landau Theory
 Order Parameter
 Critical exponents and Universality
IV The Arrow of Time
 Hamiltonian dynamics and phase space
 Liouville's theorem
 Coarse graining
 The master equation
 Random walks and the diffusion equation
 Detailed balance
 Brownian motion and the Langevin equation
 Dynamics of fluctuations
 Fluctuationdissipation relations and Linear Response

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2021/22, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Supervised Practical/Workshop/Studio Hours 11,
Summative Assessment Hours 2,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
61 )

Assessment (Further Info) 
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %

Additional Information (Assessment) 
Degree Examination, 100%
Visiting Student Variant Assessment
Degree Examination, 100% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Define and distinguish between the Boltzmann and Gibbs entropies, and derive the principal ensembles of Statistical Physics by using the method of Lagrange multipliers to maximise the Gibbs entropy.
 Discuss the manybody problem and effect of interactions and be able to formulate and motivate various approximation schemes.
 Discuss and formulate fluctuationdissipation relations
 Formulate the Ising model of phase transitions and be able to motivate and work out various meanfield theories such as Landau theory.
 Articulate the paradox of the arrow of time; formulate and solve mathematical descriptions of dynamics such as the master equation, Langevin equations and the diffusion equation.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  StatP 
Contacts
Course organiser  Prof Martin Evans
Tel: (0131 6)50 5294
Email: M.Evans@ed.ac.uk 
Course secretary  Ms Grace Wilson
Tel: (0131 6)50 5310
Email: Grace.Wilson@ed.ac.uk 

