Vol. 2 No. 1 (2018)
Research Articles

A Correspondence Principle

Barry D. Hughes
School of Mathematics and Statistics, University of Melbourne, Victoria 3010 Australia
Barry W. Ninham
Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, ACT 0200, Australia

Published 2018-03-26


  • classical analysis,
  • quantum mechanics,
  • statistical mechanics,
  • random walks and Lévy flights,
  • quasicrystals,
  • Casimir forces
  • ...More

How to Cite

Hughes, B. D., & Ninham, B. W. (2018). A Correspondence Principle. Substantia, 2(1), 51–76. https://doi.org/10.13128/Substantia-41


A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical “correspondence principle”, a kind of wave–particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative cases discussed are drawn from classical and anomalous diffusion, quantum mechanics of single particles and ideal gases, quasicrystals and Casimir forces.

Permission to reproduce: Republished from Physica A, 2016, 443, 495-517. With permission from Elsevier. Copyright 2016