Correlations and screening of topological charges in Gaussian random fields
Correlations and screening of topological charges in Gaussian random fields
Two-point topological charge correlation functions of several types of geometric singularity in Gaussian random fields are calculated explicitly, using a general scheme: zeros of n-dimensional random vectors, signed by the sign of their Jacobian determinant; critical points (gradient zeros) of real scalars in two dimensions signed by the Hessian; and umbilic points of real scalars in two dimensions, signed by their index. The functions in each case depend on the underlying spatial correlation function of the field. These topological charge correlation functions are found to obey the first Stillinger-Lovett sum rule for ionic fluids.
6611-6628
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61
2003
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61
Dennis, M.R.
(2003)
Correlations and screening of topological charges in Gaussian random fields.
Journal of Physics A: Mathematical and General, 36 (24), .
(doi:10.1088/0305-4470/36/24/301).
Abstract
Two-point topological charge correlation functions of several types of geometric singularity in Gaussian random fields are calculated explicitly, using a general scheme: zeros of n-dimensional random vectors, signed by the sign of their Jacobian determinant; critical points (gradient zeros) of real scalars in two dimensions signed by the Hessian; and umbilic points of real scalars in two dimensions, signed by their index. The functions in each case depend on the underlying spatial correlation function of the field. These topological charge correlation functions are found to obey the first Stillinger-Lovett sum rule for ionic fluids.
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Published date: 2003
Organisations:
Applied Mathematics
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Local EPrints ID: 29383
URI: http://eprints.soton.ac.uk/id/eprint/29383
ISSN: 0305-4470
PURE UUID: 92fa6fcf-bb07-4d0d-947d-0db13c6f416d
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Date deposited: 12 May 2006
Last modified: 15 Mar 2024 07:31
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M.R. Dennis
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