The Landauer Resistance and Band Spectra for the Counting Quantum Turing Machine

Abstract

The generalized counting quantum Turing machine (GCQTM) is a machine which, for any N, enumerates the first $2^{N}$ integers in succession as binary strings. The generalization consists of associating a potential with read-1 steps only. The Landauer Resistance (LR) and band spectra were determined for the tight binding Hamiltonians associated with the GCQTM for energies both above and below the potential height. For parameters and potentials in the electron region, the LR fluctuates rapidly between very high and very low values as a function of momentum. The rapidity and extent of the fluctuations increases rapidly with increasing N. For N=18, the largest value considered, the LR shows good transmission probability as a function of momentum with numerous holes of very high LR values present. This is true for energies above and below the potential height. It is suggested that the main features of the LR can be explained by coherent superposition of the component waves reflected from or transmitted through the $2^{N-1}$ potentials in the distribution. If this explanation is correct, it provides a dramatic illustration of the effects of quantum nonlocality.