On the generators of quantum stochastic evolution equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 1, pp. 46-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A characterisation of the stochastic bounded generators of quantum irreversible wave equations is given. This suggests the general form of quantum stochastic evolution with respect to the Poisson (jumps), Wiener (diffusion) or general Quantum Noise. The corresponding irreversible Heisenberg evolution in terms of stochastic completely positive maps is found and the general form of the stochastic completely dissipative operator equation is discovered.
@article{TMF_1997_110_1_a3,
     author = {V. P. Belavkin},
     title = {On the generators of quantum stochastic evolution equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {46--60},
     year = {1997},
     volume = {110},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a3/}
}
TY  - JOUR
AU  - V. P. Belavkin
TI  - On the generators of quantum stochastic evolution equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1997
SP  - 46
EP  - 60
VL  - 110
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a3/
LA  - ru
ID  - TMF_1997_110_1_a3
ER  - 
%0 Journal Article
%A V. P. Belavkin
%T On the generators of quantum stochastic evolution equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1997
%P 46-60
%V 110
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a3/
%G ru
%F TMF_1997_110_1_a3
V. P. Belavkin. On the generators of quantum stochastic evolution equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 1, pp. 46-60. http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a3/

[1] G. Lindblad, Commun. Math. Phys., 48 (1976), 119–130 | DOI | MR | Zbl

[2] D. E. Evans, J. T. Lewis, Commun. Dublin Institute for Advanced Studies, 24 (1977), 104 | Zbl

[3] V. P. Belavkin, UMN, 47:1 (1992), 47–106 | MR | Zbl

[4] R. S. Hudson, K. R. Parthasarathy, Commun. Math. Phys., 93 (1984), 301–323 | DOI | MR | Zbl

[5] V. P. Belavkin, Russ. J. Math. Phys., 3:4 (1995), 523–528 | MR | Zbl

[6] V. P. Belavkin, “Nondemolition Measurements and Nonlinear Filtering of Quantum Stochastic Processes”, Lecture Notes in Control and Information Sciences, 121, Springer-Verlag, 1988, 245–266 | DOI | MR

[7] V. P. Belavkin, “Nondemolition Calculus and Nonlinear Filtering in Quantum Systems”, Stochastic Methods in Mathematics and Physics, World Scientific, 1989, 310–324 | MR

[8] V. P. Belavkin, J. Multivariate Analysis, 42:2 (1992), 171–201 | DOI | MR | Zbl

[9] N. Gisin, Phys. Rev. Lett., 52 (1984), 1657–1660 | DOI | MR

[10] L. Diosi, Phys. Rev., A40 (1988), 1165–1174

[11] A. Barchielli, V. P. Belavkin, J. Phys. A: Math. Gen., 24 (1991), 1495–1514 | DOI | MR

[12] V. P. Belavkin, Commun. Math. Phys., 146 (1992), 611–635 | DOI | MR | Zbl

[13] H. Carmichael, Open Systems in Quantum Optics, Lecture Notes in Physics, 18, Springer-Verlag, 1993 | MR

[14] G. Milburn, Phys. Rev. A, 36 (1987), 744 | DOI | MR

[15] P. Pearle, Phys. Rev. D, 29 (1984), 235 | DOI | MR

[16] G. C. Ghirardi, P. Pearle, A. Rimini, Phys. Rev. A, 42 (1990), 78–89 | DOI | MR

[17] V. P. Belavkin, J. Math. Phys., 31 (1990), 2930–2934 | DOI | MR | Zbl

[18] V. P. Belavkin, J. Phys. A: Math. Gen., 22 (1989), L1109–1114 | DOI | MR

[19] M. J. Collett, C. W. Gardiner, Phys. Rev. A, 31 (1985), 3761–3774 | DOI | MR

[20] V. P. Belavkin, Mat. zametki, 49:6 (1991), 135–137 | MR | Zbl