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Electron Transport Through One-Dimensional Quantum Systems

BROWSE_DETAIL_CREATION_DATE: 07-12-2017

BROWSE_DETAIL_IDENTIFIER_SECTION

BROWSE_DETAIL_TYPE: Thesis

BROWSE_DETAIL_SUB_TYPE: Masters

BROWSE_DETAIL_PUBLISH_STATE: Unpublished

BROWSE_DETAIL_FORMAT: PDF Document

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: Physics,

BROWSE_DETAIL_CREATORS: Algadi, Latifa (Author),

BROWSE_DETAIL_CONTRIBUTERS: Oymak, Hüseyin (Advisor),

BROWSE_DETAIL_TAB_KEYWORDS

Electron transport, quantum transport, one-dimensional quantum systems, scattering problems, transmission and reection, delta-function potentials, Diracnotation, atomic chains, atomic rings, resonance, antiresonance, Aharonov-Bohmrings, Ricatti-ratios method


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We study the quantum transport of an electron through some one-dimensional (1D)quantum systems (or seemingly 2D systems which are practically reducible to 1Dsystems) coupled to two ideal leads. After reviewing the rudiments of electricity phenomena,leading to the concept of current, and some magnetism phenomena in termsof classical mechanics, we provide the basic formalism of quantum mechanics byelucidating its working machinery in terms of Dirac notation. We next deal with 1Dscattering problems and study in detail some examples containing delta-function potentials.We then focus on the so-called two-state quantum systems, like the ammoniamolecule, the hydrogen molecular ion, and the hydrogen molecule. Later onwe investigate the propagation of an electron in a 1D crystal lattice with all of itsne details. After settling down the rudiments of 1D nite linear atomic-chain andatomic-ring structures, we come to the subject of resonant transport that we investigatethrough some illustrative problems. We then present the mathematics and physicsof the Aharonov-Bohm (AB) rings, for which we touch the classical Lagrangian andHamiltonian dynamics for a charged particle moving in an electromagnetic eld andthe relevant gauge transformations. Finally, for obtaining transport properties of 1Dquantum systems, we demonstrate how to use a pruning technique, called Ricattiratiosmethod, which changes the time-independent discrete Schr ¨odinger equationinto a two-point recursive equation. We test the method in some 1D well-knownviisystems as well as in single and double AB rings by simply reducing them to onedimension with the help of a decimation method.


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