dorsal/arxiv
View SchemaVolume Elements of Monotone Metrics on the n x n Density Matrices as Densities-of-States for Thermodynamic Purposes. I
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9711010 |
| URL | https://arxiv.org/abs/quant-ph/9711010 |
Abstract
Among 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.
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"abstract": "Among the monotone metrics on the (n^{2} - 1)-dimensional convex set of n x n\ndensity matrices, as Petz and Sudar have recently elaborated, there are a\nminimal (Bures) and a maximal one. We examine the proposition that it is\nphysically meaningful to treat the volume elements of these metrics as\ndensities-of-states for thermodynamic purposes. In the n = 2 (spin-1/2) case,\nuse of the maximal monotone metric, in fact, does lead to the adoption of the\nLangevin (and not the Brillouin) functions, thus, completely conforming with a\nrecent probabilistic argument of Lavenda. Brody and Hughston also arrived at\nthe Langevin function in an analysis based on the Fubini-Study metric. It is a\nmatter of some interest, however, that in the first (subsequently modified)\nversion of their paper, they had reported a different result, one fully\nconsistent with the alternative use of the minimal monotone metric. In this\npart I of our investigation, we first study scenarios involving partially\nentangled spin-1/2 particles (n = 4, 6,...) and then a certain three-level\nextension of the two-level systems. In part II, we examine, in full generality,\nand with some limited analytical success, the cases n = 3 and 4.",
"arxiv_id": "quant-ph/9711010",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"title": "Volume Elements of Monotone Metrics on the n x n Density Matrices as Densities-of-States for Thermodynamic Purposes. I",
"url": "https://arxiv.org/abs/quant-ph/9711010"
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