A Correspondence Principle

  • Barry D. Hughes School of Mathematics and Statistics, University of Melbourne, Victoria 3010 Australia http://orcid.org/0000-0003-3594-4303
  • Barry W. Ninham Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, ACT 0200, Australia http://orcid.org/0000-0001-5706-1988
Keywords: classical analysis, quantum mechanics, statistical mechanics, random walks and Lévy flights, quasicrystals, Casimir forces

Abstract

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

Author Biographies

Barry D. Hughes, School of Mathematics and Statistics, University of Melbourne, Victoria 3010 Australia

He is a member of the School of Mathematics and Statistics of the University of Melbourne. His current or recent research interests are in modelling cell motion in developmental biology and in other contexts; stochastic modelling (including random walk processes, random environments, power-law phenomena, and stochastically evolving networks); methods of applied mathematics (especially transform methods and asymptotics); continuuum modelling (most recently in biological contexts, but formerly using continuum mechanics methodologies in colloid and interface science)

Barry W. Ninham, Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, ACT 0200, Australia

Barry Ninham was educated at Guildford Grammar School, St Georges College and the University of Western Australia. He was one of the first of the cohort of Australians who went to the USA rather than the UK for graduate education. In so doing he gave up the chance to be in the Australian 1960 Rome Olympics Crew. Barry founded the ANU Department of "Applied Mathematics" in 1970. It became a world leader in the field of colloid and surface science, a subject that underlies all of modern biology and chemical engineering. He also founded and led the ANU Department of Optical Sciences Department. His work and contributions have been recognised in numerous honours and awards from Sweden, Japan, France, Russia, Germany, USA and Australia.

Published
2018-03-26
How to Cite
Hughes, B., & Ninham, B. (2018). A Correspondence Principle. Substantia, 2(1), 51-76. https://doi.org/10.13128/Substantia-41
Section
Research Articles