On the long time behavior of free stochastic Schrödinger evolutions

Bassi, A., Dürr, D. and Kolb, M. (2010) On the long time behavior of free stochastic Schrödinger evolutions. Reviews in Mathematical Physics, 22 (1). pp. 55-89. ISSN 0129-055X doi: 10.1142/S0129055X10003886

Abstract/Summary

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.