ArticleOriginal scientific text

Title

Stochastic Dynamics of Quantum Spin Systems

Authors 1, 2, 3

Affiliations

  1. Institute of Theoretical Physics and Astrophysics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
  2. Institute of Theoretical Physics, University of Wrocław, pl. Maksa Borna 9, 50-204 Wrocław, Poland
  3. Mathematics Department, Imperial College, 180 Queen's Gate, London, SW7 2BZ, UK

Abstract

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

Bibliography

  1. L. Accardi, Topics in Quantum Probability, Phys. Rep. 77 (1981), 169-192.
  2. L. Accardi and C. Cecchini, Conditional Expectations in von Neumann Algebras and a Theorem of Takesaki, J. Func. Anal. 45 (1982), 245-273.
  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).
  4. A. Connes, Sur le Théorème de Radon-Nikodym pour les Poids Normaux Fidèles Semi-finis, Bull. Sc. math., 2e série, 97 (1973), 253-258.
  5. H. Epstein, Remarks on Two Theorems of E. Lieb, Commun. Math. Phys. 31 (1973), 317-325.
  6. E. H. Lieb, Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture, Adv. in Math. 11 (1973), 267-288.
  7. A. W. Majewski and B. Zegarliński, On Quantum Stochastic Dynamics and Noncommutative Lp Spaces, Lett. Math. Phys. 36 (1995), 337-349.
  8. A.W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics I: Spin Systems on a Lattice, Math. Phys. Electronic J. 1 (1995), Paper 2.
  9. A.W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics II, Rev. Math. Phys. 8 (1996), 689-713.
  10. A.W. Majewski and B. Zegarliński, On quantum stochastic dynamics, Markov Proc. and Rel. Fields 2 (1996), 87-116.
  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.
  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.
  13. T. Matsui, Markov semigroups which describe the time evolution of some higher spin quantum models, J. Func. Anal. 116 (1993), 179-198.
  14. R. Olkiewicz and B. Zegarliński, Hypercontractive Markov Semigroups in Noncommutative Lp Spaces, Preprint 1997.
  15. G. Stragier, J. Quaegebeur and A. Verbeure, Quantum detailed balance, Ann. Inst. Henri Poincaré 41 (1984), 25-36.
Pages:
285-295
Main language of publication
English
Published
1998
Exact and natural sciences