Constructing quantum dissipations and their reversible states from classical interacting spin systems

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1. [1] R. Carmona, Wen Chen Master and B. Simon, Relativistic Schrödinger Operators: Asymptotic Behavior of the Eigenfunctions, J. Funct. Anal., Vol. 91, 1990, pp. 117-142. Zbl0716.35006MR1054115
2. [2] J. Glimm and A. Jaffe, Quantum Physics. A Functional Integral Point of View, Springer-Verlag, New York/Heidelberg/Berlin, 1981. Zbl0461.46051MR628000
3. [3] B. Simon, Functional Integration and Quantum Physics, New York, Academic Press, 1979. Zbl0434.28013MR544188
4. [4] E. Nelson, Feynman Integrals and the Schrödinger Equation, J. Math. Phys., Vol. 5, 1964, pp. 332-343. Zbl0133.22905MR161189
5. [5] W. Driessler, L. Landau and J. Fernando Perez, Estimates of Critical Lengths and Critical Temperatures for Classical and Quantum Lattice Systems, J. Stat. Phys., Vol. 20, 1979, pp. 123-162. MR523638
6. [6] H. Spohn and R. Dümcke, Quantum Tunneling with Dissipation and the Ising Model over R, J. Stat. Phys., Vol. 41, 1985, pp. 389-423. MR814839
7. [7] A. Alastuey and Ph. A Martin, Absence of exponential clustering in quantum Coulomb fluids, Preprint, 1989. MR1028965
8. [8] T. Matsui, Uniqueness of the translationally invariant ground state in quantum spin systems, Comm. Math. Phys., Vol. 126, 1990, pp. 453-467. Zbl0691.46055MR1032868
9. [9] V. Gorini, A. Kossakowski and E.C.G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys., Vol. 17, 1976, p. 821. MR406206
10. [10] A. Frigerio, V. Gorini, A. Kossakowski and M. Verri, Quantum detailed balance and the KMS condition, Comm. Math. Phys., Vol. 57, 1977, pp. 97-110. Zbl0374.46060MR468989
11. [11] G. Lindblad, On the generators of dynamical semigroups, Comm. Math. Phys., Vol. 48, 1976, p. 119. Zbl0343.47031MR413878
12. [12] J. Quaegebeur, G. Stragier and A. Verbeure, Quantum detailed balance, Ann. Inst. Henri Poincaré, Vol. 41, 1984, p. 25. Zbl0581.46065MR760124
13. [13] J. Quaegebeur and A. Verbeure, Relaxation of the bose-gas, Lett. Matt. Phys., Vol. 9, 1985, p. 93. MR785861
14. [14] G. Stragier, De detailed balance voorwaarde en thermodynamisch evenwicht, Ph. D. Thesis, KUL, 1984. 
15. [15] H.O. Georgii, Gibbs Measures and Phase Transitions, De Gruyter Studies in Mathematics, 1988. Zbl0657.60122MR956646
16. [16] T. Liggett, Interacting Particle Systems, Springer Verlag, New York, 1985. Zbl0559.60078MR776231
17. [17] O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. I and II, Springer-Verlag, 1979, 1981. Zbl0463.46052
18. [18] R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics, 286, Springer-Verlag, New York, 1981. Zbl0652.46055MR911678
19. [19] M. Fannes, P. Vanheuverzwijn and A. Verbeure, Energy-Entropy Inequalities for classical lattice systems, J. Stat. Phys., Vol. 29, 1982, pp. 541-595. MR704587
20. [20] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975. Zbl0308.47002MR493420
21. [21] M. Fannes and A. Verbeure, Global thermodynamic stability and correlation inequalities, J. Math. Phys., Vol. 19, 1978, p. 558. MR484203