Relativistic Impacts on Electrical Resistance of a One‐Dimensional Finite Crystal

Roy, C.L.; Basu, Chandan

doi:10.1002/pssb.2221770207

Cited by 6 publications

(1 citation statement)

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“…Transmission properties of 1-D structures for which the potential distributions are initial segments of substitution sequences have also been studied [12][13][14][15][16]. Of special interest here are studies of the Landauer Resistance [17,18] for various potential distributions and its relation to the band structure of infinite periodic systems whose unit cells are initial segments of substitution sequences [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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

Benioff

1997

Phys. Rev. B

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Abstract1-D systems with deterministic disorder, such as those with quasiperiodic or substitution sequence potential distributions, have been much studied. It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states in some basis B, that are computable and are thus periodic or have deterministic disorder. These generalized machines (GQTMs) can be used to investigate the effect of potentials in causing reflections and reducing the completion probability of computations. This paper expands on this work by determining the spectral and transmission properties of an example GQTM, which enumerates the integers in succession as binary strings. A potential is associated with just one type of step. For many computation paths the potential distributions are initial segments of a distribution that is quasiperiodic and corresponds to a substitution sequence. Thus the methods developed in the study of 1-D systems can be used to calculate the energy band spectra and Landauer Resistance (LR). For energies below the barrier height, The LR fluctuates rapidly with momentum with minima close to or at band-gap edges. Also for several values of the parameters involved there is good transmission over some momentum regions.

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