We show that recently introduced noncommutative -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.
@article{bwmeta1.element.bwnjournal-article-bcpv43i1p285bwm, author = {Majewski, Adam and Olkiewicz, Robert and Zegarli\'nski, Bogus\l aw}, title = {Stochastic Dynamics of Quantum Spin Systems}, journal = {Banach Center Publications}, volume = {43}, year = {1998}, pages = {285-295}, zbl = {0979.46048}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p285bwm} }
Majewski, Adam; Olkiewicz, Robert; Zegarliński, Bogusław. Stochastic Dynamics of Quantum Spin Systems. Banach Center Publications, Tome 43 (1998) pp. 285-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p285bwm/
[000] [1] L. Accardi, Topics in Quantum Probability, Phys. Rep. 77 (1981), 169-192.
[001] [2] L. Accardi and C. Cecchini, Conditional Expectations in von Neumann Algebras and a Theorem of Takesaki, J. Func. Anal. 45 (1982), 245-273. | Zbl 0483.46043
[002] [3] O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer Verlag, New York-Heidelberg-Berlin, vol. I (1979), vol. II (1981). | Zbl 0421.46048
[003] [4] A. Connes, Sur le Théorème de Radon-Nikodym pour les Poids Normaux Fidèles Semi-finis, Bull. Sc. math., série, 97 (1973), 253-258.
[004] [5] H. Epstein, Remarks on Two Theorems of E. Lieb, Commun. Math. Phys. 31 (1973), 317-325. | Zbl 0257.46089
[005] [6] E. H. Lieb, Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture, Adv. in Math. 11 (1973), 267-288. | Zbl 0267.46055
[006] [7] A. W. Majewski and B. Zegarliński, On Quantum Stochastic Dynamics and Noncommutative Spaces, Lett. Math. Phys. 36 (1995), 337-349. | Zbl 0846.46044
[007] [8] A.W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics I: Spin Systems on a Lattice, Math. Phys. Electronic J. 1 (1995), Paper 2. | Zbl 0827.58064
[008] [9] A.W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics II, Rev. Math. Phys. 8 (1996), 689-713. | Zbl 0863.46041
[009] [10] A.W. Majewski and B. Zegarliński, On quantum stochastic dynamics, Markov Proc. and Rel. Fields 2 (1996), 87-116. | Zbl 0876.46041
[010] [11] A.W. Majewski, R. Olkiewicz and B. Zegarliński, Dissipative dynamics for quantum spin systems on a lattice, in: Frontiers in Quantum Physics, Eds. S. C. Lim, R. Abd-Shukor, K. H. Kwek, Springer Verlag, 1998, 112-126. | Zbl 0917.46059
[011] [12] A.W. Majewski, R. Olkiewicz and B. Zegarliński, Construction and ergodicity of dissipative dynamics for quantum spin systems on a lattice, J. Phys. A: Math. Gen. 31 (1998), 2045-2056. | Zbl 0917.46059
[012] [13] T. Matsui, Markov semigroups which describe the time evolution of some higher spin quantum models, J. Func. Anal. 116 (1993), 179-198. | Zbl 0795.47029
[013] [14] R. Olkiewicz and B. Zegarliński, Hypercontractive Markov Semigroups in Noncommutative Spaces, Preprint 1997.
[014] [15] G. Stragier, J. Quaegebeur and A. Verbeure, Quantum detailed balance, Ann. Inst. Henri Poincaré 41 (1984), 25-36. | Zbl 0581.46065