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It was recently shown that a generalization of quantum Turing machines(QTMs), in which potentials are associated with elementary steps or transitionsof the computation, generates potential distributions along computation pathsof states in some basis B. The distributions are computable and are thusperiodic or have deterministic disorder. These generalized machines (GQTMs) canbe used to investigate the effect of potentials in causing reflections andreducing the completion probability of computations. This work is extended hereby determination of the spectral and transmission properties of an example GQTMwhich enumerates the integers as binary strings. A potential is associated withjust one type of step. For many computation paths the potential distributionsare initial segments of a quasiperiodic distribution that corresponds to asubstitution sequence. The energy band spectra and Landauer Resistance (LR) arecalculated for energies below the barrier height by use of transfer matrices.The LR fluctuates rapidly with momentum with minima close to or at band-gapedges. For several values of the parameters, there is good transmission oversome momentum regions.Comment: 22 pages Latex, 13 postscript figures, Submitted to Phys. Rev.

Transmission and spectral aspects of tight-binding Hamiltonians for the counting quantum Turing machine