dorsal/arxiv
View SchemaScattering in quantum tubes
| Authors | B. Nilsson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103029 |
| URL | https://arxiv.org/abs/quant-ph/0103029 |
| DOI | 10.1142/9789812810809_0021 |
Abstract
It is possible to fabricate mesoscopic structures where at least one of the dimensions is of the order of de Broglie wavelength for cold electrons. By using semiconductors, composed of more than one material combined with a metal slip-gate, two-dimensional quantum tubes may be built. We present a method for predicting the transmission of low-temperature electrons in such a tube. This problem is mathematically related to the transmission of acoustic or electromagnetic waves in a two-dimensional duct. The tube is asymptotically straight with a constant cross-section. Propagation properties for complicated tubes can be synthesised from corresponding results for more simple tubes by the so-called Building Block Method. Conformal mapping techniques are then applied to transform the simple tube with curvature and varying cross-section to a straight, constant cross-section, tube with variable refractive index. Stable formulations for the scattering operators in terms of ordinary differential equations are formulated by wave splitting using an invariant imbedding technique. The mathematical framework is also generalised to handle tubes with edges, which are of large technical interest. The numerical method consists of using a standard MATLAB ordinary differential equation solver for the truncated reflection and transmission matrices in a Fourier sine basis. It is proved that the numerical scheme converges with increasing truncation.
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"abstract": "It is possible to fabricate mesoscopic structures where at least one of the\ndimensions is of the order of de Broglie wavelength for cold electrons. By\nusing semiconductors, composed of more than one material combined with a metal\nslip-gate, two-dimensional quantum tubes may be built. We present a method for\npredicting the transmission of low-temperature electrons in such a tube. This\nproblem is mathematically related to the transmission of acoustic or\nelectromagnetic waves in a two-dimensional duct. The tube is asymptotically\nstraight with a constant cross-section. Propagation properties for complicated\ntubes can be synthesised from corresponding results for more simple tubes by\nthe so-called Building Block Method. Conformal mapping techniques are then\napplied to transform the simple tube with curvature and varying cross-section\nto a straight, constant cross-section, tube with variable refractive index.\nStable formulations for the scattering operators in terms of ordinary\ndifferential equations are formulated by wave splitting using an invariant\nimbedding technique. The mathematical framework is also generalised to handle\ntubes with edges, which are of large technical interest. The numerical method\nconsists of using a standard MATLAB ordinary differential equation solver for\nthe truncated reflection and transmission matrices in a Fourier sine basis. It\nis proved that the numerical scheme converges with increasing truncation.",
"arxiv_id": "quant-ph/0103029",
"authors": [
"B. Nilsson"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/9789812810809_0021",
"title": "Scattering in quantum tubes",
"url": "https://arxiv.org/abs/quant-ph/0103029"
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