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Screening of charged singularities of random fields

Wilkinson, Michael (2004). Screening of charged singularities of random fields. Journal of Physics A: Mathematical and General, 37 pp. 6763–6771.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1088/0305-4470/37/26/012
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Abstract

Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of plus or minus one. In random fields we can define a correlation function for the charge-weighted density of singularities. In many types of random fields, this correlation function satisfies an identity which shows that the singularities 'screen' each other perfectly: a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge, and vice-versa. This paper gives a simple and widely applicable derivation of this result. A counterexample where screening is incomplete is also exhibited.

Item Type: Journal Article
ISSN: 0305-4470
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 3494
Depositing User: Michael Wilkinson
Date Deposited: 27 Jun 2006
Last Modified: 02 Dec 2010 19:49
URI: http://oro.open.ac.uk/id/eprint/3494
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