journal article Mar 01, 1987

The essentially commutative dilations of dynamical semigroups onM n

View at Publisher Save 10.1007/bf01205670
Topics

No keywords indexed for this article. Browse by subject →

References
23
[1]
Albeverio, S., Hoegh-Krohn, R., Olsen, G.: Dynamical semigroups and Markov processes onC*-algebras. J. Reine Angew. Math.319, 25–37 (1980)
[2]
Albeverio, S., Hoegh-Krohn, R.: A remark on dynamical semigroups in terms of diffusion processes. In: Quantum probability and applications II. Proceedings, Heidelberg 1984, Lecture Notes in Mathematics Vol.1136, pp. 40–45. Berlin, Heidelberg, New York: Springer 1985 10.1007/bfb0074457
[3]
Alicki, R., Fannes, M.: Dilations of quantum dynamical semigroups with classical Brownian motion. Commun. Math. Phys. (in press) 10.1007/bf01212314
[4]
Davies, E. B.: Dilations of completely positive maps. J. Lond. Math. Soc. (2)17, 330–338 (1978) 10.1112/jlms/s2-17.2.330
[5]
Emch, G. G., Albeverio, S., Eckmann, J.-P.: Quasi-free generalizedK-flows. Rep. Math. Phys.13, 73–85 (1978) 10.1016/0034-4877(78)90021-6
[6]
Evans, D. E.: Positive linear maps on operator algebras. Commun. Math. Phys.48, 15–22 (1976) 10.1007/bf01609408
[7]
Evans, D. E.: Completely positive quasi-free maps on the CAR algebra. Commun. Math. Phys.70, 53–68 (1979) 10.1007/bf01220502
[8]
Evans, D. E., Lewis, J. T.: Dilations of dynamical semi-groups. Commun. Math. Phys.50, 219–227 (1976) 10.1007/bf01609402
[9]
Evans, D. E., Lewis, J. T.: Dilations of irreversible evolutions in algebraic quantum theory. Commun. Dublin Inst. Adv. Stud. Ser.A24 (1977)
[10]
Frigerio, A., Gorini, V.: On stationary Markov dilations of quantum dynamical semigroups; Frigerio, A, Gorini, V.: Markov dilations and quantum detailed balance. Commun. Math. Phys.93, 517–532 (1984) 10.1007/bf01212293
[11]
Frigerio, A.: Covariant Markov dilations of quantum dynamical semigroups. Preprint, Milano 1984 10.1007/bf01212293
[12]
Hudson, R. L. Parthasarathy, K. R.: Quantum Ito's formula and stochastic evolutions. Commun. Math. Phys.93, 301–323 (1984) 10.1007/bf01258530
[13]
Hunt, G. A.: Semi-groups of measures on Lie groups. Trans. Am. Math. Soc.81, 264–293 (1956) 10.1090/s0002-9947-1956-0079232-9
[14]
Kossakowski, A., Frigerio, A., Gorini, V., Verri, M.: Quantum detailed balance and KMS condition. Commun. Math. Phys.57, 97–110 (1977) 10.1007/bf01625769
[15]
Kümmerer, B.: A Dilation theory for completely positive operators onW*-algebras. Thesis, Tübingen 1982;
[16]
Kümmerer, B.: Markov dilations onW*-algebras. J. Funct. Anal.63, 139–177 (1985) 10.1016/0022-1236(85)90084-9
[17]
Kümmerer, B.: A non-commutative example of a continuous Markov dilation. Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 1982/83, pp. 61–91;
[18]
Kümmerer, B.: Examples of Markov dilations over the 2 × 2 matrices. In: Quantum probability and applications to the quantum theory of irreversible processes. Proceedings, Villa Mondragone 1982, Lecture Notes in Mathematics Vol.1055, pp. 228–244. Berlin, Heidelberg, New York: Springer 1984 10.1007/bfb0071725
[19]
Kümmerer, B.: On the structure of Markov dilations onW*-algebras. In: Quantum probability and applications II. Proceedings, Heidelberg, 1984, Lecture Notes in Mathematics Vol.1136, pp. 332–347. Berlin, Heidelberg, New York: Springer 1985 10.1007/bfb0074483
[20]
Kümmerer, B., Schröder, W.: A new construction of unitary dilations: Singular coupling to white noise. In: Quantum probability and applications II. Proceedings, Heidelberg 1984, Lecture Notes in Mathematics Vol.1136, pp. 332–347. Berlin, Heidelberg, New York: Springer 1985 10.1007/bfb0074483
[21]
Lewis, J. T., Thomas, L. C.: How to make a heat bath. In: Functional integration, Proceedings Cumberland Lodge 1974, pp. 97–123, London: Oxford University Press (Clarendon) 1975
[22]
On the generators of quantum dynamical semigroups

G. Lindblad

Communications in Mathematical Physics 1976 10.1007/bf01608499
[23]
Maassen, H.: Quantum Markov processes on Fock space described by integral kernels. In: Quantum probability and applications II. Proceedings, Heidelberg 1984, Lecture Notes in Mathematics Vol.1136, pp. 361–374, Berlin, Heidelberg, New York: Springer 1985 10.1007/bfb0074485
Metrics
63
Citations
23
References
Details
Published
Mar 01, 1987
Vol/Issue
109(1)
Pages
1-22
License
View
Cite This Article
Burkhard Kümmerer, Hans Maassen (1987). The essentially commutative dilations of dynamical semigroups onM n. Communications in Mathematical Physics, 109(1), 1-22. https://doi.org/10.1007/bf01205670
Related

You May Also Like

Particle creation by black holes

S. W. Hawking · 1975

10,628 citations

On the generators of quantum dynamical semigroups

G. Lindblad · 1976

6,183 citations

The four laws of black hole mechanics

J. M. Bardeen, B. Carter · 1973

3,127 citations

Non-abelian bosonization in two dimensions

Edward Witten · 1984

1,940 citations

Intermittent transition to turbulence in dissipative dynamical systems

Yves Pomeau, PAUL MANNEVILLE · 1980

1,701 citations