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?
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| 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: Fermi-Dirac, Bose-Einstein, classical limit
- Bose-Einstein Condensation
II The Many-Body Problem
- Interacting systems
- Phonons and the Debye theory of specific heat of solids
- Perturbation theory and cluster expansion
- Breakdown of perturbation theory
- Non-perturbative ideas: Debye-H\"uckel Theory
III Transitions
- Phenomenology of phase transitions
- The Ising Model
- Solution in one dimension
- Correlation functions and correlation length
- Mean-field 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
- Fluctuation-dissipation relations and Linear Response
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| 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
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2015/16, Available to all students (SV1)
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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 )
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| 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 many-body problem and be able to formulate and motivate various approximation schemes.
4) Describe the phenomenology of phase transitions
in particular Bose-Einstein condensation, liquid-gas transition and ferromagnetic ordering.
5) Formulate the Ising model of phase transitions and be able to motivate and work out various mean-field 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 fluctuation-dissipation relations and linear correlation and response theory
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | StatP |
Contacts
| Course organiser | Prof Arjun Berera
Tel: (0131 6)50 5246
Email: |
Course secretary | Ms Rebecca Thomas
Tel: (0131 6)50 7218
Email: |
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