dorsal/arxiv
View SchemaA rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion
| Authors | Bernhard Bodmann, Hajo Leschke, Simone Warzel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810069 |
| URL | https://arxiv.org/abs/quant-ph/9810069 |
| Journal | pp. 173-176 in: Path Integrals from peV to TeV: 50 Years after Feynman's Paper, Editors: R. Casalbuoni, R.Giachetti, V.Tognetti, R. Vaia, P.Verrucchi, World Scientific, Singapore, 1999 |
Abstract
Adapting ideas of Daubechies and Klauder we derive a continuum path-integral formula for the time evolution generated by a spin Hamiltonian. For this purpose we identify the finite-dimensional spin Hilbert space with the ground-state eigenspace of a suitable Sch\"odinger operator on $L^2({\mathbb{R}}^2)$, the Hilbert space of square-integrable functions on the Euclidean plane ${\mathbb{R}}^2$, and employ the Feynman-Kac-It\^o formula.
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"abstract": "Adapting ideas of Daubechies and Klauder we derive a continuum path-integral\nformula for the time evolution generated by a spin Hamiltonian. For this\npurpose we identify the finite-dimensional spin Hilbert space with the\nground-state eigenspace of a suitable Sch\\\"odinger operator on\n$L^2({\\mathbb{R}}^2)$, the Hilbert space of square-integrable functions on the\nEuclidean plane ${\\mathbb{R}}^2$, and employ the Feynman-Kac-It\\^o formula.",
"arxiv_id": "quant-ph/9810069",
"authors": [
"Bernhard Bodmann",
"Hajo Leschke",
"Simone Warzel"
],
"categories": [
"quant-ph"
],
"journal_ref": "pp. 173-176 in: Path Integrals from peV to TeV: 50 Years after\n Feynman\u0027s Paper, Editors: R. Casalbuoni, R.Giachetti, V.Tognetti, R. Vaia,\n P.Verrucchi, World Scientific, Singapore, 1999",
"title": "A rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion",
"url": "https://arxiv.org/abs/quant-ph/9810069"
},
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