Stochastic Schrödinger evolution and symmetric Kähler manifolds of low dimension

Details Stochastic Schrödinger evolution and symmetric Kähler manifolds of low dimension Stochastic Schrödinger evolution and symmetric Kähler manifolds of low dimension

2002-12-18

arxiv.org/abs/quant-ph/0212107v1

Physics

Quantum Physics

latex, 23 pages

Scientific paper

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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