Journal of Statistical Physics

, Volume 58, Issue 5–6, pp 1209–1230 | Cite as

Model apparatus for quantum measurements

  • Bernard Gaveau
  • L. S. Schulman
Articles

Abstract

We present a model system that behaves as a measurement apparatus for quantum systems should. The device is macroscopic, it interacts with the microscopic system to be measured, and the results of that interaction affect the macroscopic device in a macroscopic, irreversible way. Everything is treated quantum mechanically: the apparatus is defined in terms of its (many) coordinates, the Hamiltonian is given, and time evolution follows Schrödinger's equation. It is proposed that this model be itself used as a laboratory for testing ideas on the measurement process.

Key words

Quantum measurement theory apparatus models 

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References

  1. 1.
    L. S. Schulman,Phys. Lett. A 102:396 (1984).Google Scholar
  2. 2.
    L. S. Schulman,J. Stat. Phys. 42:689 (1986).Google Scholar
  3. 3.
    L. S. Schulman,Phys. Lett. A 130:194 (1988);Ann. Phys. 183:320 (1988); Remote twotime boundary conditions and special states in quantum mechanics,Found. Phys. Lett., to appear; Semiclassical two-time localization and the consequences of restrictions on wave packet spreading, preprint.Google Scholar
  4. 4.
    F. Benatti, G. C. Ghirardi, A. Rimini, and T. Weber,Nuovo Cimento B 100:27 (1987); P. Pearle,Phys. Rev. D 13:857 (1976); P. Pearle,Phys. Rev. A 39:2277 (1989); D. Bohm and J. Bub,Rev. Mod. Phys. 38:453 (1966).Google Scholar
  5. 5.
    K. Hepp,Helv. Phys. Acta 45:237 (1972).Google Scholar
  6. 6.
    J. S. Bell,Helv. Phys. Acta 48:93 (1975).Google Scholar
  7. 7.
    K. Gottfried,Quantum Mechanics (Benjamin, New York, 1966), Section 20.3.Google Scholar
  8. 8.
    H. S. Green,Nuovo Cimento 9:880 (1958).Google Scholar
  9. 9.
    N. G. van Kampen,Physica A 153:97 (1988).Google Scholar
  10. 10.
    G. T. Zimanyi and K. Vladar,Phys. Rev. A 34:3496 (1986); G. T. Zimanyi and K. Vladar, Symmetry breaking and measurement theory,Found. Phys. Lett. 1:175 (1988).Google Scholar
  11. 11.
    P. W. Anderson, Measurement in quantum theory and the problem of complex systems, inThe Lesson of Quantum Theory, J. de Boer, E. Dal, and O. Ulfbeck, eds. (Elsevier, 1986).Google Scholar
  12. 12.
    A. O. Caldeira and A. J. Leggett,Phys. Rev. Lett. 46:211 (1981);Ann. Phys. 149:374 (1983).Google Scholar
  13. 13.
    M. Aizenman, J. T. Chayes, L. Chayes, and C. M. Newman,J. Stat. Phys. 50:1 (1988); C. M. Newman and L. S. Schulman,Commun. Math. Phys. 104:547 (1986).Google Scholar
  14. 14.
    P. W. Milonni, J. R. Ackerhalt, H. W. Galbraith, and M.-L. Shih,Phys. Rev. A 28:32 (1983).Google Scholar
  15. 15.
    J. Ford,J. Math. Phys. 2:387 (1961).Google Scholar
  16. 16.
    P. Bocchieri and A. Loinger,Phys. Rev. 107:337 (1957).Google Scholar
  17. 17.
    L. S. Schulman,Phys. Rev. A 18:2379 (1978).Google Scholar
  18. 18.
    E. P. Wigner, Interpretation of quantum mechanics, inQuantum Theory and Measurement, J. A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton, New Jersey, 1983).Google Scholar
  19. 19.
    J. A. Wheeler and W. H. Zurek, eds.,Quantum Theory and Measurement (Princeton University Press, Princeton, New Jersey, 1983).Google Scholar
  20. 20.
    A. Daneri, A. Loinger, and G. M. Prosperi,Nucl. Phys. 33:297 (1962).Google Scholar
  21. 21.
    W. H. Zurek,Phys. Rev. D 26:1862 (1982).Google Scholar
  22. 22.
    R. J. Glauber, Amplifiers, attenuators, and Schrödinger's cat, inNew Techniques and Ideas in Quantum Measurement Theory, D. M. Greenberger, ed. (New York Academy of Science, New York, 1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Bernard Gaveau
    • 1
  • L. S. Schulman
    • 2
  1. 1.MathematiquesUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Physics DepartmentClarkson UniversityPotsdam

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