Volume Elements of Monotone Metrics on the n x n Density Matrices as Densities-of-States for Thermodynamic Purposes. I

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dc.creatorSlater, Paul B.
dc.date1997-11-10
dc.date1998-12-07
dc.date.accessioned2026-07-07T06:14:31Z
dc.date.available2026-07-07T06:14:31Z
dc.descriptionAmong the monotone metrics on the (n^{2} - 1)-dimensional convex set of n x n density matrices, as Petz and Sudar have recently elaborated, there are a minimal (Bures) and a maximal one. We examine the proposition that it is physically meaningful to treat the volume elements of these metrics as densities-of-states for thermodynamic purposes. In the n = 2 (spin-1/2) case, use of the maximal monotone metric, in fact, does lead to the adoption of the Langevin (and not the Brillouin) functions, thus, completely conforming with a recent probabilistic argument of Lavenda. Brody and Hughston also arrived at the Langevin function in an analysis based on the Fubini-Study metric. It is a matter of some interest, however, that in the first (subsequently modified) version of their paper, they had reported a different result, one fully consistent with the alternative use of the minimal monotone metric. In this part I of our investigation, we first study scenarios involving partially entangled spin-1/2 particles (n = 4, 6,...) and then a certain three-level extension of the two-level systems. In part II, we examine, in full generality, and with some limited analytical success, the cases n = 3 and 4.
dc.description13 pages, LaTeX. We retitle and slightly modify the paper. For Part II (the cases of spin-1 and spin-3/2 particles), see quant-ph/9802019
dc.identifierhttps://arxiv.org/abs/quant-ph/9711010
dc.identifierhttp://arxiv.org/abs/quant-ph/9711010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93492
dc.subjectQuantum Physics
dc.titleVolume Elements of Monotone Metrics on the n x n Density Matrices as Densities-of-States for Thermodynamic Purposes. I
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