---
_id: '45765'
author:
- first_name: Robert
  full_name: Grummt, Robert
  last_name: Grummt
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Grummt R, Kolb M. Essential selfadjointness of singular magnetic Schrödinger
    operators on Riemannian manifolds. <i> Journal of Mathematical Analysis and Applications</i>.
    2012;388:480-489. doi:<a href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>
  apa: Grummt, R., &#38; Kolb, M. (2012). Essential selfadjointness of singular magnetic
    Schrödinger operators on Riemannian manifolds. <i> Journal of Mathematical Analysis
    and Applications</i>, <i>388</i>, 480–489. <a href="https://doi.org/10.1016/j.jmaa.2011.09.060">https://doi.org/10.1016/j.jmaa.2011.09.060</a>
  bibtex: '@article{Grummt_Kolb_2012, title={Essential selfadjointness of singular
    magnetic Schrödinger operators on Riemannian manifolds}, volume={388}, DOI={<a
    href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>},
    journal={ Journal of Mathematical Analysis and Applications}, author={Grummt,
    Robert and Kolb, Martin}, year={2012}, pages={480–489} }'
  chicago: 'Grummt, Robert, and Martin Kolb. “Essential Selfadjointness of Singular
    Magnetic Schrödinger Operators on Riemannian Manifolds.” <i> Journal of Mathematical
    Analysis and Applications</i> 388 (2012): 480–89. <a href="https://doi.org/10.1016/j.jmaa.2011.09.060">https://doi.org/10.1016/j.jmaa.2011.09.060</a>.'
  ieee: 'R. Grummt and M. Kolb, “Essential selfadjointness of singular magnetic Schrödinger
    operators on Riemannian manifolds,” <i> Journal of Mathematical Analysis and Applications</i>,
    vol. 388, pp. 480–489, 2012, doi: <a href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>.'
  mla: Grummt, Robert, and Martin Kolb. “Essential Selfadjointness of Singular Magnetic
    Schrödinger Operators on Riemannian Manifolds.” <i> Journal of Mathematical Analysis
    and Applications</i>, vol. 388, 2012, pp. 480–89, doi:<a href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>.
  short: R. Grummt, M. Kolb,  Journal of Mathematical Analysis and Applications 388
    (2012) 480–489.
date_created: 2023-06-26T08:04:27Z
date_updated: 2023-06-26T08:04:47Z
department:
- _id: '96'
doi: 10.1016/j.jmaa.2011.09.060
intvolume: '       388'
language:
- iso: eng
page: 480-489
publication: ' Journal of Mathematical Analysis and Applications'
status: public
title: Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian
  manifolds
type: journal_article
user_id: '14931'
volume: 388
year: '2012'
...
---
_id: '37500'
abstract:
- lang: eng
  text: '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.'
author:
- first_name: Angelo
  full_name: Bassi, Angelo
  last_name: Bassi
- first_name: Detlef
  full_name: Dürr, Detlef
  last_name: Dürr
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: 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>
  apa: 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>
  bibtex: '@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} }'
  chicago: '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>.'
  ieee: '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>.'
  mla: 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>.
  short: A. Bassi, D. Dürr, M. Kolb, Reviews in Mathematical Physics 22 (2009) 55–89.
date_created: 2023-01-19T06:49:37Z
date_updated: 2023-01-19T06:49:46Z
department:
- _id: '96'
doi: https://doi.org/10.1142/S0129055X10003886
intvolume: '        22'
issue: '1'
language:
- iso: eng
page: 55-89
publication: Reviews in Mathematical Physics
publication_status: published
status: public
title: ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS
type: journal_article
user_id: '85821'
volume: 22
year: '2009'
...