Dynamics of a pair of interacting spins coupled to an environmental sea

International Journal of Modern Physics B

Volumn 12, Issue 11, 1998, Pages 1191-1245

  Dube M ^a,b   Stamp, P C E ^c,d  

^a HELSINKI INSTITUTE OF PHYSICS   (Finland)

^b AALTO UNIVERSITY   (Finland)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^d MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000628876     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979298000661     Document Type: Article

References (42)

1. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. A, Zwerger, Rev. Mod. Phys. 59, 1 (1987).
2. N. V. Prokof'ev and P. C. E. Stamp, J. Phys. Condensed Matter 5, L663 (1993).
3. P. C. E. Stamp, Physica B197, 133 (1994).
4. N. V. Prokof'ev and P. C. E. Stamp, pp. 347-371 in Quantum Tunneling of Magnetisation - QTM '94, eds. L. Gunther and B. Barbara (Kluwer Publishing, Dordrecht, 1995).
5. N. V. Prokof'ev and P. C. E. Stamp, J. Low Temp. Phys. 104, 143 (1996).
6. N. V. Prokof'ev and P. C. E. Stamp, UBC preprint (April 1995)/cond-mat 9511011.
7. A. Schmid, J. Low. Temp. Phys. 49, 609 (1982).
8. A. O. Caldeira and A. J. Leggett, Physica 121A, 587 (1983).
9. A. O. Caldeira and A. J. Leggett, Phys. Rev. A, 1059 (1985).
10. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993).
11. Y. C. Chen, J. Low Temp. Phys. 65, 133 (1986).
12. M. Dubé and P. C. E. Stamp, in preparation.
13. J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton Univ. Press, 1983); J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge Univ. Press, 1987).
14. J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton Univ. Press, 1983); J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge Univ. Press, 1987).
15. A. J. Leggett, Prog. Theo. Phys. Supp. 69, 80 (1980).
16. A. J. Leggett, pp. 396-507 in "Matter and Chance: Proc. 1986 les Houches Summer School", eds. J. Souletie, J. Vannimenus and R. Stora (North-Holland, Amsterdam 1987); and A. J. Leggett, in Frontiers and Borderlines in Many-Particle Physics, eds. R. A. Broglia and J. R. Schrieffer (North-Holland, Amsterdam, 1988).
17. A. J. Leggett, pp. 396-507 in "Matter and Chance: Proc. 1986 les Houches Summer School", eds. J. Souletie, J. Vannimenus and R. Stora (North-Holland, Amsterdam 1987); and A. J. Leggett, in Frontiers and Borderlines in Many-Particle Physics, eds. R. A. Broglia and J. R. Schrieffer (North-Holland, Amsterdam, 1988).
18. M. Dubé, E. Mueller and P. C. E. Stamp, in preparation; see also E. Mueller, UBC undergraduate thesis (March 1996).
19. M. Dubé, E. Mueller and P. C. E. Stamp, in preparation; see also E. Mueller, UBC undergraduate thesis (March 1996).
20. S. Chakravarty and J. Hirsch, Phys. Rev. B25, 3273 (1982).
21. F. Sols and P. Bhattacharyya, Phys. Rev. B38, 12 263 (1988).
22. See A. Matro and J. A. Cini, J. Phys. Chem. 99, 2568 (1995), and refs therein.
23. C. P. Schlichter, "Principles of Nuclear Magnetic Resonance" (Springer-Verlag; 3rd edition, 1989); for a recent interesting application to coupled nuclei in a high magnetic field, see Y. Bychkov, T. Maniv and I. D. Vagner, Sol. Stat. Commun. 94, 61 (1995).
24. C. P. Schlichter, "Principles of Nuclear Magnetic Resonance" (Springer-Verlag; 3rd edition, 1989); for a recent interesting application to coupled nuclei in a high magnetic field, see Y. Bychkov, T. Maniv and I. D. Vagner, Sol. Stat. Commun. 94, 61 (1995).
25. For coupled 2-level systems in glasses, see S. Hunklinger and A. K. Raychaudhuri, Prog. Low Temp. Phys. 9, 267 (1986); C. C. Yu and A. J. Leggett, Comments Sol. St. Phys. 14, 231 (1989); C. C. Yu, Phys. Rev. Lett. 63, 1160 (1989); S. Coppersmith, Phys. Rev. Lett. 67, 2015 (1991); S. Burin, J. Low Temp. Phys. 100, 309 (1995).
26. For coupled 2-level systems in glasses, see S. Hunklinger and A. K. Raychaudhuri, Prog. Low Temp. Phys. 9, 267 (1986); C. C. Yu and A. J. Leggett, Comments Sol. St. Phys. 14, 231 (1989); C. C. Yu, Phys. Rev. Lett. 63, 1160 (1989); S. Coppersmith, Phys. Rev. Lett. 67, 2015 (1991); S. Burin, J. Low Temp. Phys. 100, 309 (1995).
27. For coupled 2-level systems in glasses, see S. Hunklinger and A. K. Raychaudhuri, Prog. Low Temp. Phys. 9, 267 (1986); C. C. Yu and A. J. Leggett, Comments Sol. St. Phys. 14, 231 (1989); C. C. Yu, Phys. Rev. Lett. 63, 1160 (1989); S. Coppersmith, Phys. Rev. Lett. 67, 2015 (1991); S. Burin, J. Low Temp. Phys. 100, 309 (1995).
28. For coupled 2-level systems in glasses, see S. Hunklinger and A. K. Raychaudhuri, Prog. Low Temp. Phys. 9, 267 (1986); C. C. Yu and A. J. Leggett, Comments Sol. St. Phys. 14, 231 (1989); C. C. Yu, Phys. Rev. Lett. 63, 1160 (1989); S. Coppersmith, Phys. Rev. Lett. 67, 2015 (1991); S. Burin, J. Low Temp. Phys. 100, 309 (1995).
29. For coupled 2-level systems in glasses, see S. Hunklinger and A. K. Raychaudhuri, Prog. Low Temp. Phys. 9, 267 (1986); C. C. Yu and A. J. Leggett, Comments Sol. St. Phys. 14, 231 (1989); C. C. Yu, Phys. Rev. Lett. 63, 1160 (1989); S. Coppersmith, Phys. Rev. Lett. 67, 2015 (1991); S. Burin, J. Low Temp. Phys. 100, 309 (1995).
30. K. G. Wilson, Phys. Rev. 140, B445 (1965),
31. and Phys. Rev. D2, 1438 (1970); see also K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
32. and Phys. Rev. D2, 1438 (1970); see also K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
33. R. P. Feynman and F. L. Vernon Jr., Ann. Phys. (N. Y.) 24, 118 (1963).
34. A. O. Caldeira and A. J. Leggett, Ann. Phys. (N. Y.) 149, 374 (1984).
35. A. J. Leggett, Phys. Rev. B30, 1208 (1984).
36. N. V. Prokof'ev, Phys. Rev. B49, 2148 (1994); see also Phys. Rev. Lett. 71, 2995 (1993).
37. N. V. Prokof'ev, Phys. Rev. B49, 2148 (1994); see also Phys. Rev. Lett. 71, 2995 (1993).
38. There are many discussions of the mapping to oscillator baths. A lengthy summary, with references, is in P. C. E. Stamp, pp. 373-398 in Quantum Tunneling of Magnetisation, eds. L. Gunther and B. Barbara (Kluwer, Amsterdam, 1995).
39. P. W. Anderson, G. Yuval and D. R. Hamann, Phys. Rev. B1, 4464 (1970).
40. A. J. Bray and M. A. Moore, Phys. Rev. Lett. 49, 1545 (1982).
41. J. L. Cardy, J. Phys. A14, 1407 (1981).
42. U. Weiss and M. Wollensack, Phys. Rev. Lett. 62, 1663 (1989).