| Issue |
EPL
Volume 84, Number 1, October 2008
|
|
|---|---|---|
| Article Number | 10005 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/84/10005 | |
| Published online | 16 September 2008 | |
On the long-time behavior of Hilbert space diffusion
1
Department of Theoretical Physics, University of Trieste - Strada Costiera 11, 34014 Trieste, Italy, EU
2
Mathematisches Institut der L.M.U. - Theresienstr. 39, 80333 München, Germany, EU
Corresponding author: bassi@ts.infn.it
Received:
28
May
2008
Accepted:
20
August
2008
Stochastic differential equations in Hilbert space as random nonlinear modified Schrödinger 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.
PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory / 02.50.Ey – Stochastic processes / 02.30.Jr – Partial differential equations
© EPLA, 2008
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