article published Angelo Bassi author Detlef Dürr author Martin Kolb author 48880 96 department 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. 2009 eng https://doi.org/10.1142/S0129055X10003886 22155-89 A. Bassi, D. Dürr, M. Kolb, Reviews in Mathematical Physics 22 (2009) 55–89. Bassi, Angelo, et al. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” <i>Reviews in Mathematical Physics</i>, vol. 22, no. 1, 2009, pp. 55–89, doi:<a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>. Bassi A, Dürr D, Kolb M. ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS. <i>Reviews in Mathematical Physics</i>. 2009;22(1):55-89. doi:<a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a> Bassi, A., Dürr, D., &#38; Kolb, M. (2009). ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS. <i>Reviews in Mathematical Physics</i>, <i>22</i>(1), 55–89. <a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a> Bassi, Angelo, Detlef Dürr, and Martin Kolb. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” <i>Reviews in Mathematical Physics</i> 22, no. 1 (2009): 55–89. <a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>. A. Bassi, D. Dürr, and M. Kolb, “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS,” <i>Reviews in Mathematical Physics</i>, vol. 22, no. 1, pp. 55–89, 2009, doi: <a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>. @article{Bassi_Dürr_Kolb_2009, title={ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS}, volume={22}, DOI={<a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>}, number={1}, journal={Reviews in Mathematical Physics}, author={Bassi, Angelo and Dürr, Detlef and Kolb, Martin}, year={2009}, pages={55–89} } 375002023-01-19T06:49:37Z2023-01-19T06:49:46Z