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

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q. 
Information for Visiting Students
Prerequisites  None 
Course Delivery Information

Academic year 2014/15, 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)  Statistical Physics  2:00  
Learning Outcomes
Upon successful completion of this course it is intended that a student will be able to:
1) Define and distinguish between the Boltzmann and Gibbs
entropies
2) Derive the principal ensembles of Statistical Physics
by using the method of Lagrange multipliers to maximise the Gibbs entropy
3) Discuss the manybody problem and be able to formulate and motivate various approximation schemes.
4) Describe the phenomenology of phase transitions
in particular BoseEinstein condensation, liquidgas transition and ferromagnetic ordering.
5) Formulate the Ising model of phase transitions and be able to motivate and work out various meanfield theories
6) Articulate the paradox of the arrow of time.
7) Formulate mathematical descriptions of dynamics such as Fermi's master equation, Langevin equations and the diffusion equation; solve simple examples of such descriptions such as random walks and Brownian motion
8) Discuss and formulate fluctuationdissipation relations and linear correlation and response theory

Contacts
Course organiser  Prof Arjun Berera
Tel: (0131 6)50 5246
Email: ab@ph.ed.ac.uk 
Course secretary  Ms Rebecca Thomas
Tel: (0131 6)50 7218
Email: R.Thomas@ed.ac.uk 

