On the long time behavior of Hilbert space diffusion

Abstract

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.

6 pages, EPL2-TeX

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Cited by in corpus (8)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Exact solution for a non-Markovian dissipative quantum dynamics
• Dissipative collapse models with non-white noises
• On the Electromagnetic Properties of Matter in Collapse Models
• Single particle energy diffusion from relativistic spontaneous localization
• Effects of the continuous spontaneous localization model in the regime of large localization length scale
• Comment on "Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems"
• Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: general solution and main properties