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# PHSI421 Advanced Statistical Mechanics

## Paper Description

The course aims to provide a graduate-level understanding of the physics of many-body systems. Students will develop a deeper knowledge of classical thermodynamics, and how this is connected to the statistical description of microscopic systems, both quantum and classical. The course also indroduces the key concept of phase transitions in interacting systems.

Teaching will emphasize problem-solving skills and the application of abstract concepts to concrete systems.

Prerequisites:
PHSI 331, PHSI 332

This paper consists of 15 lectures and 6 tutorials. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for PHSI421

Course Coordinator:
Dr Philip Brydon

After completing this paper students are expected to have achieved the following major learning objectives:

• Define and use free energies, be able to derive their thermodynamic identities, and extract information from thermodynamic partial derivative relations
• Understand the thermodynamics of systems undergoing a phase transition, with a detailed knowledge of the phase diagram of the van der Waals model
• Be able to define and apply the microcanonical, canonical and grand canonical ensembles appropriately, and understand the statistical basis for thermodynamic equilibrium
• Derive thermodynamic properties from a microscopic description of standard systems, e.g. ideal paramagnet, Einstein solid, ideal gas
• Be able to apply the equipartition theorem, and understand its regime of validity
• Be able to explain the effect indistinguishability has on the statistical properties of matter. Derive and apply the quantum distribution functions
• Apply the appropriate quantum statistical method to calculate the thermal properties of the standard quantum systems: an ideal Fermi Gas, photons in a cavity, and an ideal Bose gas. Derive and apply the appropriate density of states for these systems
• Solve the Ising model using the mean-field approximation

Topics:

• Review: Basic thermal concepts and ideal gases.
• Review: 2nd Law of Thermodynamics and the microcanonical ensemble.
• Review: Definition of entropy and equilibration for weakly coupled systems.
• Free energies as a force toward equilibrium for open systems. Thermodynamic identities and dreivative relations. Basic chemical thermodynamics.
• Phase transitions of pure substances. Van der Waals model.
• Canonical ensemble: Boltzmann statistics and the partition function.
• Grand canonical ensemble: Gibbs factors, occupation number representation for bosons and fermions, and distribution functions.
• Degenerate Fermi gas.
• Blackbody radiation.
• Bose-Einstein condensation
• Ising Model of a Ferromagnet. Phase transitions and critical exponents.

Resources:
Textbook: An introduction to thermal physics, Daniel V. Schroeder, Addison Wesley Longman

# Formal University Information

The following information is from the University’s corporate web site.

## Details

Advanced topics in many-body physics: the quantum ideal gas, classical and quantum transport phenomena, and phase transitions in interacting systems.

Paper title Advanced Statistical Mechanics PHSI421 Physics 0.0833 10 points Semester 1 (On campus) \$704.22 Tuition Fees for international students are elsewhere on this website.
Limited to
BSc(Hons), PGDipSci, MSc
Contact
philip.brydon@otago.ac.nz
Teaching staff
Dr Philip Brydon
Textbooks

An introduction to thermal physics, Daniel V. Schroeder, Addison Wesley Longman.

Graduate Attributes Emphasised
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
View more information about Otago's graduate attributes.
Learning Outcomes
After completing this paper students are expected to have achieved the following major learning objectives:
• Define and use free energies, be able to derive their thermodynamic identities, and extract information from thermodynamic partial derivative relations
• Understand the thermodynamics of systems undergoing a phase transition, with a detailed knowledge of the phase diagram of the van der Waals model
• Be able to define and apply the microcanonical, canonical and grand canonical ensembles appropriately and understand the statistical basis for thermodynamic equilibrium
• Derive thermodynamic properties from a microscopic description of standard systems (e.g. ideal paramagnet, Einstein solid, ideal gas)
• Be able to apply the equipartition theorem and understand its regime of validity
• Be able to explain the effect indistinguishability has on the statistical properties of matter; derive and apply the quantum distribution functions
• Apply the appropriate quantum statistical method to calculate the thermal properties of the standard quantum systems: an ideal Fermi gas, photons in a cavity, and an ideal Bose gas; derive and apply the appropriate density of states for these systems
• Solve the Ising model using the mean-field approximation

## Timetable

### Semester 1

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None