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, then_Q^N(t)=exp(–1H_N^Qt)_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 interval aroundt₃,t₆,,t_3N, the machine part of_Q^N(t) is stationary.