ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS
A. Bassi, D. Dürr, M. Kolb, Reviews in Mathematical Physics 22 (2009) 55–89.
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Bassi, Angelo;
Dürr, Detlef;
Kolb, MartinLibreCat
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Abstract
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.
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Journal Title
Reviews in Mathematical Physics
Volume
22
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1
Page
55-89
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Bassi A, Dürr D, Kolb M. ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS. Reviews in Mathematical Physics. 2009;22(1):55-89. doi:https://doi.org/10.1142/S0129055X10003886
Bassi, A., Dürr, D., & Kolb, M. (2009). ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS. Reviews in Mathematical Physics, 22(1), 55–89. https://doi.org/10.1142/S0129055X10003886
@article{Bassi_Dürr_Kolb_2009, title={ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS}, volume={22}, DOI={https://doi.org/10.1142/S0129055X10003886}, number={1}, journal={Reviews in Mathematical Physics}, author={Bassi, Angelo and Dürr, Detlef and Kolb, Martin}, year={2009}, pages={55–89} }
Bassi, Angelo, Detlef Dürr, and Martin Kolb. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” Reviews in Mathematical Physics 22, no. 1 (2009): 55–89. https://doi.org/10.1142/S0129055X10003886.
A. Bassi, D. Dürr, and M. Kolb, “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS,” Reviews in Mathematical Physics, vol. 22, no. 1, pp. 55–89, 2009, doi: https://doi.org/10.1142/S0129055X10003886.
Bassi, Angelo, et al. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” Reviews in Mathematical Physics, vol. 22, no. 1, 2009, pp. 55–89, doi:https://doi.org/10.1142/S0129055X10003886.
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