Stochastic Dynamics of Quantum Spin Systems

Adam Majewski; Robert Olkiewicz; Bogusław Zegarliński

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 285-295
  • ISSN: 0137-6934

Abstract

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We show that recently introduced noncommutative L p -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.

How to cite

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Majewski, Adam, Olkiewicz, Robert, and Zegarliński, Bogusław. "Stochastic Dynamics of Quantum Spin Systems." Banach Center Publications 43.1 (1998): 285-295. <http://eudml.org/doc/208849>.

@article{Majewski1998,
abstract = {We show that recently introduced noncommutative $L_p$-spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.},
author = {Majewski, Adam, Olkiewicz, Robert, Zegarliński, Bogusław},
journal = {Banach Center Publications},
keywords = {noncommutative -spaces; Markov semigroups; quantum systems on a lattice},
language = {eng},
number = {1},
pages = {285-295},
title = {Stochastic Dynamics of Quantum Spin Systems},
url = {http://eudml.org/doc/208849},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Majewski, Adam
AU - Olkiewicz, Robert
AU - Zegarliński, Bogusław
TI - Stochastic Dynamics of Quantum Spin Systems
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 285
EP - 295
AB - We show that recently introduced noncommutative $L_p$-spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.
LA - eng
KW - noncommutative -spaces; Markov semigroups; quantum systems on a lattice
UR - http://eudml.org/doc/208849
ER -

References

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  1. [1] L. Accardi, Topics in Quantum Probability, Phys. Rep. 77 (1981), 169-192. 
  2. [2] L. Accardi and C. Cecchini, Conditional Expectations in von Neumann Algebras and a Theorem of Takesaki, J. Func. Anal. 45 (1982), 245-273. Zbl0483.46043
  3. [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). Zbl0421.46048
  4. [4] A. Connes, Sur le Théorème de Radon-Nikodym pour les Poids Normaux Fidèles Semi-finis, Bull. Sc. math., 2 e série, 97 (1973), 253-258. 
  5. [5] H. Epstein, Remarks on Two Theorems of E. Lieb, Commun. Math. Phys. 31 (1973), 317-325. Zbl0257.46089
  6. [6] E. H. Lieb, Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture, Adv. in Math. 11 (1973), 267-288. Zbl0267.46055
  7. [7] A. W. Majewski and B. Zegarliński, On Quantum Stochastic Dynamics and Noncommutative L p Spaces, Lett. Math. Phys. 36 (1995), 337-349. Zbl0846.46044
  8. [8] A.W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics I: Spin Systems on a Lattice, Math. Phys. Electronic J. 1 (1995), Paper 2. Zbl0827.58064
  9. [9] A.W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics II, Rev. Math. Phys. 8 (1996), 689-713. Zbl0863.46041
  10. [10] A.W. Majewski and B. Zegarliński, On quantum stochastic dynamics, Markov Proc. and Rel. Fields 2 (1996), 87-116. Zbl0876.46041
  11. [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. Zbl0917.46059
  12. [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. Zbl0917.46059
  13. [13] T. Matsui, Markov semigroups which describe the time evolution of some higher spin quantum models, J. Func. Anal. 116 (1993), 179-198. Zbl0795.47029
  14. [14] R. Olkiewicz and B. Zegarliński, Hypercontractive Markov Semigroups in Noncommutative L p Spaces, Preprint 1997. 
  15. [15] G. Stragier, J. Quaegebeur and A. Verbeure, Quantum detailed balance, Ann. Inst. Henri Poincaré 41 (1984), 25-36. Zbl0581.46065

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