dorsal/arxiv
View SchemaThe Landauer Resistance and Band Spectra for the Counting Quantum Turing Machine
| Authors | Paul Benioff |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9702021 |
| URL | https://arxiv.org/abs/quant-ph/9702021 |
| DOI | 10.1016/S0167-2789(98)00041-4 |
| Journal | Physica D120 (1998) 12-29 |
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.
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"abstract": "The generalized counting quantum Turing machine (GCQTM) is a machine which,\nfor any N, enumerates the first $2^{N}$ integers in succession as binary\nstrings. The generalization consists of associating a potential with read-1\nsteps only. The Landauer Resistance (LR) and band spectra were determined for\nthe tight binding Hamiltonians associated with the GCQTM for energies both\nabove and below the potential height. For parameters and potentials in the\nelectron region, the LR fluctuates rapidly between very high and very low\nvalues as a function of momentum. The rapidity and extent of the fluctuations\nincreases rapidly with increasing N. For N=18, the largest value considered,\nthe LR shows good transmission probability as a function of momentum with\nnumerous holes of very high LR values present. This is true for energies above\nand below the potential height. It is suggested that the main features of the\nLR can be explained by coherent superposition of the component waves reflected\nfrom or transmitted through the $2^{N-1}$ potentials in the distribution. If\nthis explanation is correct, it provides a dramatic illustration of the effects\nof quantum nonlocality.",
"arxiv_id": "quant-ph/9702021",
"authors": [
"Paul Benioff"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0167-2789(98)00041-4",
"journal_ref": "Physica D120 (1998) 12-29",
"title": "The Landauer Resistance and Band Spectra for the Counting Quantum Turing Machine",
"url": "https://arxiv.org/abs/quant-ph/9702021"
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