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

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^Qt)ψ_Q^N(0) correctly describes at timest₃,t₆,⋯,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 aroundt₃,t₆,⋯,t_3N, the "machine" part ofψ_Q^N(t) is stationary.