Aims
Aim
Having successfully completed this module, you will be able to:
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Microcanonical ensemble (e.g. enumerate microstates for some simple physical systems.)
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Understand the microscopic definition of entropy and temperature
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Canonical ensemble; apply it to some simple physical systems immersed in a heath bath (temperature)
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Understand the probabilistic interpretation of entropy, heat and work
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Understand the importance of quantum mechanics for a correct statistical description in terms of Fermi and Bose gases and their applications:�
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Acquire an understanding of the chemical potential
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Distinguish between Bose and Fermi gases and their ground states
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Understand how Bose-Einstein condensation leads to unique states of matter at low temperatures
• 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
Assessment methods
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."
| Method | Hours | Percentage contribution |
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| 10 Problem Sheets | - | 20% |
| Exam | 2 hours | 80% |
Referral Method: See notes below
By examination, the final mark will be calculated both with and without the coursework assessment mark carried forward, and the higher result taken.