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


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(−1H N Qt)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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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

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

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