Solomon, A. I.; Blasiak, P.; Duchamp, G. E. H.; Horzela, A. and Penson, K. A.
(2004).
Partition functions and graphs: A combinatorial approach.
In: Proceedings of the XI International Conference on Symmetry Methods in Physics (SYMPHYS-11), 21-24 June 2004, Prague.
Full text available as:
Abstract
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman{type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a super uid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequence of graphs analogous to zero{dimensional Feynman diagrams. [brace not closed]
| Item Type: |
Conference Item
|
| Copyright Holders: |
2004 The Author |
| Keywords: |
boson normal ordering; combinatorics |
| Academic Unit/Department: |
Science > Physical Sciences |
| Item ID: |
20814 |
| Depositing User: |
Astrid Peterkin
|
| Date Deposited: |
23 Mar 2010 10:49 |
| Last Modified: |
06 Dec 2010 18:22 |
| URI: |
http://oro.open.ac.uk/id/eprint/20814 |
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