Many Particle Systems

Much of modern physics is concerned with explanation of macroscopic phenomena in terms of the underlying behaviour of the atoms or molecules which are the microscopic elements of the many-particle system. Although it is true that, at the microscopic level, the world as we know it obeys the laws of quantum mechanics, our everyday experience forces us to think about systems which are large, and for which the actual rules that govern the microscopic behaviour are secondary to those imposed by the sheer size of the system. For example, even a single grain of sand contains of the order of 10²⁰ molecules of SiO₂ and so we need to ask what large scale behaviour or collective properties does such a system have. Some of these so-called macroscopic properties are so general that they are meaningful for all systems. Concepts such as energy, temperature and pressure are familiar examples. Less familiar is the idea of entropy and this turns out to be the fundamental key to understanding the link between the microscopic structure and the macroscopic behaviour.

This course sets out to establish a deep understanding of the general properties of macroscopic systems from a microscopic viewpoint, with the concept of entropy playing a central role. Building on a small number of simple ideas it develops the basis of statistical thermodynamics. The relationship to classical thermodynamics is made clear and tools are developed which reveal the full power of thermodynamic argument. Having established the central importance of the macroscopic thermodynamic parameters, the course addresses the question of how these might be calculated in specific systems. The basic tools of statistical mechanics are revealed and compared with the more direct, but much more restricted ideas of kinetic theory.

The course is a fundamental building block essential to subsequent studies of all of condensed matter physics, whether it be superconductivity or pulsar physics, lasers or even life itself.

Course Outline

Assignment 1

Assignment 1 Solutions

Assignment 2

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Assignment 3

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Assignment 4

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Assignment 5

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Assignment 6

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Assignment 7

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Assignment 8

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Assignment 9

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Assignment 10

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