Classical systems, standard quantum systems, and mixed quantum systems in Hilbert space

K K Wan, J Bradshaw, Colin Trueman, F E Harrison

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Traditionally, there has been a dent distinction between classical systems and quantum systems, particularly in the mathematical theories used to describe them. In our recent work on macroscopic quantum systems, this distinction has become blurred, making a unified mathematical formulation desirable, so as to show lip both the similarities and the fundamental differences between quantum and classical systems. This paper serves this purpose, with explicit formulations and a number of examples in the form of superconducting circuit systems. We introduce three classes of physical systems with finite degrees of freedom: classical, standard quantum, and mired quantum, and present a unified Hilbert space treatment of all three types of system. We consider the classical/quantum divide and the relationship between standard quantum and mired quantum systems, illustrating the latter with a derivation of a superselection rule in superconducting systems.

Original languageEnglish
Pages (from-to)1739-1783
Number of pages45
JournalFoundations of Physics
Issue number12
Publication statusPublished - Dec 1998




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