dorsal/arxiv
View SchemaStochastic Schr\"odinger evolution and symmetric K\"ahler manifolds of low dimension
| Authors | L. P. Hughston, K. P. Tod |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212107 |
| URL | https://arxiv.org/abs/quant-ph/0212107 |
Abstract
We consider the manifold-valued, stochastic extension of the Schr\"odinger equation introduced by Hughston (Proc.Roy.Soc.Lond. A452 (1996) 953) in a manifestly covariant, differential-geometric framework, and examine the resulting quantum evolution on some specific examples of K\"ahler manifolds with many symmetries. We find conditions on the curvature for the evolution to be a `collapse process' in the sense of Brody and Hughston (Proc.Roy.Soc.Lond. A458 (2002) 1117) or, more generally, a `reduction process', and give examples that satisfy these conditions. For some of these examples, we show that the L\"uders projection postulate admits a consistent interpretation and remains valid in the nonlinear regime.
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"abstract": "We consider the manifold-valued, stochastic extension of the Schr\\\"odinger\nequation introduced by Hughston (Proc.Roy.Soc.Lond. A452 (1996) 953) in a\nmanifestly covariant, differential-geometric framework, and examine the\nresulting quantum evolution on some specific examples of K\\\"ahler manifolds\nwith many symmetries. We find conditions on the curvature for the evolution to\nbe a `collapse process\u0027 in the sense of Brody and Hughston (Proc.Roy.Soc.Lond.\nA458 (2002) 1117) or, more generally, a `reduction process\u0027, and give examples\nthat satisfy these conditions. For some of these examples, we show that the\nL\\\"uders projection postulate admits a consistent interpretation and remains\nvalid in the nonlinear regime.",
"arxiv_id": "quant-ph/0212107",
"authors": [
"L. P. Hughston",
"K. P. Tod"
],
"categories": [
"quant-ph",
"gr-qc"
],
"title": "Stochastic Schr\\\"odinger evolution and symmetric K\\\"ahler manifolds of low dimension",
"url": "https://arxiv.org/abs/quant-ph/0212107"
},
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