Journal of Statistical Physics

, Volume 22, Issue 5, pp 563–591 | Cite as

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

  • Paul Benioff
Articles

Abstract

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianHNQ and a class of appropriate initial states such that if c is such an initial state, thenψQN(t)=exp(−1HNQt)ψQN(0) correctly describes at timest3,t6,⋯,t3N model states that correspond to the completion of the first, second, ⋯, Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time intervalΔ aroundt3,t6,⋯,t3N, the “machine” part ofψQN(t) is stationary.

Key words

Computer as a physical system microscopic Hamiltonian models of computers Schrödinger equation description of Turing machines Coleman model approximation closed conservative system quantum spin lattices 

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References

  1. 1.
    M. Kac,Am. Math. Monthly 54 (1957).Google Scholar
  2. 2.
    M. Dresden and F. Feiock,J. Stat. Phys. 4:111 (1972).Google Scholar
  3. 3.
    A. Muriel,Am. J. Phys. 45:701 (1977).Google Scholar
  4. 4.
    J. von Neumann,The Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, N.J., 1955), Chapter VI.Google Scholar
  5. 5.
    G. Emch,Helv. Phys. Acta 45:1049 (1972); Whitten-Wolfe and G. Emch,Helv. Phys. Acta 49:45 (1976).Google Scholar
  6. 6.
    J. S. Bell,Helv. Phys. Acta 48:93 (1975).Google Scholar
  7. 7.
    A. Shimony,Am. J. Phys. 31:755 (1963).Google Scholar
  8. 8.
    C. Patton and J. Wheeler,Include the Observer in the Wave Function?, Preprint.Google Scholar
  9. 9.
    I. Prigogine,Science 201:777 (1978).Google Scholar
  10. 10.
    R. Landauer,IBM J. Res. Dev. 5:183 (1961).Google Scholar
  11. 11.
    R. Landauer and J. W. F. Woo,J. Appl. Phys. 42:2301 (1971).Google Scholar
  12. 12.
    R. W. Keyes and R. Landauer,IBM J. Res. Dev. 14:152 (1970).Google Scholar
  13. 13.
    R. Landauer,Ber. Bunsenges. Phys. Chem. 80:1048 (1976).Google Scholar
  14. 14.
    C. H. Bennett,IBM J. Res. Dev. 17:525 (1973).Google Scholar
  15. 15.
    H. J. Bremermann,Part I: Limitations on Data Processing Arising from Quantum Theory, inSelf-Organizing Systems, M. C. Yovits, G. T. Jacobi, and G. D. Goldstein, eds. (Spartan Books, Washington, D.C., 1962);Complexity and Transcomputability, in theEncyclopedia of Ignorance, R. Duncan and M. Weston-Smith, eds. (Pergamon Press, Oxford, England, 1977), pp. 167–174.Google Scholar
  16. 16.
    Martin Davis,Computability and Unsolvability (McGraw-Hill, New York, 1958).Google Scholar
  17. 17.
    Hartley Rogers, Jr.,Theory of Recursive Functions and Effective Computability (McGraw-Hill, New York, 1967).Google Scholar
  18. 18.
    K. Hepp,Helv. Phys. Acta 45:237 (1972).Google Scholar
  19. 19.
    P. J. Davis,Am. Math. Monthly 79:252 (1972).Google Scholar
  20. 20.
    T. Kato,Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1966), pp. 495–497.Google Scholar
  21. 21.
    F. J. Dyson,Phys. Rev. 75:486, 1736 (1949); see also S. S. Schweber,Relativistic Quantum Field Theory (Row Peterson, Illinois, 1961), Section 11f.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Paul Benioff
    • 1
  1. 1.Centre de Physique Théorique, Section IICNRSMarseillesFrance

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