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Cambridge University Press eBooks

Many particles

Jonathan Dimock

Published Feb 3, 2011• 0 citations
Publisher
DOI
10.1017/cbo9780511793349.007

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Based on the composite particle representation presented in the last paper (I), a method of solving the many-body problem known as the composite particle approximation is proposed. It is shown that a many-body system can be simplified to a composite particle system (plus one or more uncorrelated basic particles if any existed) if the following conditions are satisfied: 1) the binding energies of the composite particles are much larger than the excitation energies of the system; 2) there is domination of the collective mode for the composite particles. The interactions between the composite particles, as well as the interactions between composite particles and the basic particles can be evaluated from the original particle-particle interactions. Applications of this theory are indicated.
A general physical system is a compound system consisting of many constituents. A constituent may be made up of more than one particle, e.g., a molecule is made of atoms which themselves are made up of many particles. In a superconductor at low temperatures the electrons form pairs. 1 Each pair can be treated as a constituent of a superconducting current. For convenience we also call these constituents particles . A general physical system is referred to as a many-particle system. The theory for many-particle systems can be built up from one-particle theory. The situation can be complicated since there are different types of many-particle systems: A compound system may consists of a definite number of particles, i.e., the number of particles in the system remains the same for all time. Such a system may consist of distinguishable particles, or identical, i.e., indistinguishable, particles. 560 A compound system may consists of an indefinite number of particles, i.e., the number of particles in the system may change in time due to interactions. The particles involved may or may not be identical.