The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines
Abstract
In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each number N and Turing machine Q there exists a Hamiltonian H _{N} ^{Q} and a class of appropriate initial states such that if c is such an initial state, then ψ _{Q} ^{N} (t)=exp(1 H _{ N } ^{Q} t) ψ _{Q} ^{N} (0) correctly describes at times t _{3}, t _{6},⋯, t _{3N} model states that correspond to the completion of the first, second, ⋯, Nth computation step of Q. The model parameters can be adjusted so that for an arbitrary time interval ∆ around t _{3}, t _{6},⋯, t _{3N}, the "machine" part of ψ _{Q} ^{N} (t) is stationary.
 Publication:

Journal of Statistical Physics
 Pub Date:
 May 1980
 DOI:
 10.1007/BF01011339
 Bibcode:
 1980JSP....22..563B
 Keywords:

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