2008/09/16 by Angelo Bassi, Detlef Duerr, D. Dürr · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Differential equation #Gaussian #Hilbert space #Mathematical analysis #Mathematics #Momentum (technical analysis) #Nonlinear system #POVM #Physics #Position (finance) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum operation #Quantum state #Space time #State (computer science) #State space #Statistics #Stochastic differential equation #Stochastic partial differential equation #advanced mathematical theories #quant-ph
paper · pdf · doi:10.1209/0295-5075/84/10005
published as Europhys. Lett. 84, 10005 (2008) · 6 pages, EPL2-TeX
openalex publication_date 2008/09/16 · arxiv created 2008/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.