Scaling of nonlocal operators

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Abstract

An exact scaling relation developed for nonlocal operators is presented. The matrix elements of a general nonlocal operator are related to a set of reduced matrix elements through scaling coefficients which do not explicitly depend on the particular nonlocal operator. The theory reduces to a conventional local scaling formulation in that limit. The guide to developing the nonlocal scaling relation comes from consideration of general symmetry properties of the nonlocal operator in a chosen representation. Operators with high degrees of symmetry will generally lead to scaling relations requiring a small number of scaling coefficients for practical applications. The theory is expected to be useful not only for providing exact nonlocal scaling relations but also as a tool for developing approximate scaling relations which still retain the nonlocal nature of the operator to an appropriate extent.

Original languageEnglish (US)
Pages (from-to)877-882
Number of pages6
JournalPhysical Review A
Volume32
Issue number2
DOIs
StatePublished - Jan 1 1985

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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