On the long time behavior of Hilbert space diffusion

Details On the long time behavior of Hilbert space diffusion On the long time behavior of Hilbert space diffusion

2008-11-12

arxiv.org/abs/0811.1872v1

Europhys. Lett. 84, 10005 (2008)

Physics

Quantum Physics

6 pages, EPL2-TeX

Scientific paper

10.1209/0295-5075/84/10005

Stochastic differential equations in Hilbert space as random nonlinear modified Schroedinger equations have achieved great attention in recent years; of particular interest is the long time behavior of their solutions. In this note we discuss the long time behavior of the solutions of the stochastic differential equation describing the time evolution of a free quantum particle subject to spontaneous collapses in space. We explain why the problem is subtle and report on a recent rigorous result, which asserts that any initial state converges almost surely to a Gaussian state having a fixed spread both in position and momentum.

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