Journal of Statistical Physics

, Volume 22, Issue 5, pp 563-591

First online:

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

  • Paul BenioffAffiliated withCentre de Physique Théorique, Section II, CNRS

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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 HamiltonianH N Q and a class of appropriate initial states such that if c is such an initial state, thenψ Q N (t)=exp(−1H N Q t)ψ Q N (0) correctly describes at timest 3,t 6,⋯,t 3N 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 aroundt 3,t 6,⋯,t 3N, the “machine” part ofψ Q N (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