Screening of charged singularities of random fields
摘要
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.
引用
@article{arxiv.cond-mat/0402120,
title = {Screening of charged singularities of random fields},
author = {Michael Wilkinson},
journal= {arXiv preprint arXiv:cond-mat/0402120},
year = {2009}
}
备注
12 pages, no figures. Minor revision of manuscript submitted to J. Phys. A, August 2003