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# PHYS2024 Quantum Physics of Matter

## Module Overview

Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It leads to a microscopic interpretation of thermodynamic concepts, such as thermal equilibrium, temperature and entropy. In the course the basic principles of statistical mechanics will be introduced with applications to the physics of matter.

### Aims and Objectives

#### Module Aims

The aim of this course is to provide a general understanding of statistical mechanics which links the microscopic properties of physical systems to their macroscopic properties.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Microcanonical ensemble (e.g. enumerate microstates for some simple physical systems)
• Microscopic definition of entropy and temperature
• Canonical ensemble, and applications to some simple physical systems immersed in a heath bath (temperature)
• Probabilistic interpretation of entropy, heat and work
• Chemical potential
• How Bose-Einstein condensation leads to unique states of matter at low temperatures
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Employ quantum mechanics for a correct statistical description in terms of Fermi and Bose gases and their applications
• Distinguish between Bose and Fermi gases and their ground states

### Syllabus

- Revision of the basics laws of thermodynamics - Brief summary of combinatorics and probabilities - Discussion of basic concepts, notions and postulates of statistical mechanics e.g. microstates vs macrostates, notion of ensemble and postulate of equal a priori probability and ergodicity - Microcanonical ensemble (isolated system). From where a microscopic definition of entropy and temperature emerges. - Canonical ensemble (system in a heat reservoir). Uncover the free energy F as the natural thermodynamic potential. - Discuss the equivalence of microcanonical and canonical ensemble in the thermodynamic limit. - Applications: paramagnetism, heat capacity of solids (phonons); - Grand canonical ensemble (systems with a variable numbers of particles); Discussion of the chemical potential; - Discussion of indistinguishable particles in quantum mechanics and introduce the two types of particles: bosons and fermions - Applications: Fermi gases; zero point pressure, zero point energy, discuss the free fermion electron model - Bose gases: Black body radiation, Bose-Einstein condensation

### Learning and Teaching

TypeHours
Preparation for scheduled sessions18
Revision10
Tutorial12
Lecture36
Follow-up work18
Total study time150

S Blundell and K Blundell Ð (2006). Concepts in Thermal Physics.

R,Baierlein. Thermal Physics.

### Assessment

#### Assessment Strategy

Weekly course work will be set and assessed in the normal way, but only the best ‘n-2’ attempts will contribute to the final coursework mark. Here n is the number of course work items issued during that Semester. As an example, if you are set 10 sets of course work across a Semester, the best 8 of those will be counted. In an instance where a student may miss submitting one or two sets of course work, those sets will not be counted. Students will, however, still be required to submit Self Certification forms on time for all excused absences, as you may ultimately end up missing 3+ sets of course work through illness, for example. The submitted Self Certification forms may be considered as evidence for potential Special Considerations requests. In the event that a third (or higher) set of course work is missed, students will be required to go through the Special Considerations procedures in order to request mitigation for that set. Please note that documentary evidence will normally be required before these can be considered."

#### Summative

MethodPercentage contribution
Exam  (2 hours) 80%
Problem Sheets 20%

#### Referral

MethodPercentage contribution
Coursework marks carried forward %
Exam %

#### Repeat Information

Repeat type: Internal & External

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
PHYS1013Energy and Matter

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