2001/12/31 by Alec Maassen van den Brink, A. M. Zagoskin
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP #nlin.SI
published as Quantum Information Processing_1_, 55 (2002) · REVTeX 4, 14 p.; 1 built-in + 1 PS figure; N.B. `Alec' is my first name, `Maassen van den Brink' my family name; Pls delete the `2000' postfix to `amsmath' on l. 2 of the ms file, it's for arXiv/LANL only; v2: main text subdivided into sections, small textual changes for clarity; v3: published version with reordered sections, and figure + historical refs added
The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This is due to L only involving eigenenergydifferences_, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has rarely been mentioned in the literature, and never pursued more generally. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such L-symmetries_ are shown to occur more widely, in particular also in classical mechanics. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed.