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Connectivity-dependent Wigner delay times in molecular-scale nanostructures

Research output: Thesis › Master's Thesis

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Connectivity-dependent Wigner delay times in molecular-scale nanostructures. / Alanazy, Asma.
Lancaster University, 2016. 56 p.

Research output: Thesis › Master's Thesis

Harvard

Alanazy, A 2016, 'Connectivity-dependent Wigner delay times in molecular-scale nanostructures', MPhil, Lancaster University. https://doi.org/10.17635/lancaster/thesis/192

APA

Alanazy, A. (2016). Connectivity-dependent Wigner delay times in molecular-scale nanostructures. [Master's Thesis, Lancaster University]. Lancaster University. https://doi.org/10.17635/lancaster/thesis/192

Vancouver

Alanazy A. Connectivity-dependent Wigner delay times in molecular-scale nanostructures. Lancaster University, 2016. 56 p. doi: 10.17635/lancaster/thesis/192

Author

Alanazy, Asma. / Connectivity-dependent Wigner delay times in molecular-scale nanostructures. Lancaster University, 2016. 56 p.

Bibtex

@mastersthesis{3b7e4b0dab9844e0b4e4357b777eed7c,
title = "Connectivity-dependent Wigner delay times in molecular-scale nanostructures",
abstract = "This thesis addresses the question of the time spent by a transmitted wave packet within a scattering region. The study involves mathematical aspects of solving the Schrodinger equation in open systems with a view to developing new conceptual approaches to scattering theory. Efficient schemes to obtain scattering matrices from mean-field Hamiltonians are developed and these are implemented in new numerical codes. The relationship between the phase of S-matrix elements and Wigner delay times is also elucidated.I consider the scattering problem in a tight-binding lattice, as a simple way to understand the relation between M-functions and Greens functions and to investigate the connectivity dependence of Wigner delay times. To analyse delay times in bipartite lattices, tight binding calculations are used and a new computer code is developed to verify analytical predictions. In particular, Green{\textquoteright}s functions and a mid-gap theory are used to calculate Wigner delay times for different connectivities in graphene like molecules. One interesting and counterintuitive result is that in the weak coupling limit at the middle of HOMO and LUMO gap, the Wigner delay time does not depend on the distance between the connections to external reservoirs.",
author = "Asma Alanazy",
year = "2016",
doi = "10.17635/lancaster/thesis/192",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - THES

T1 - Connectivity-dependent Wigner delay times in molecular-scale nanostructures

AU - Alanazy, Asma

PY - 2016

Y1 - 2016

N2 - This thesis addresses the question of the time spent by a transmitted wave packet within a scattering region. The study involves mathematical aspects of solving the Schrodinger equation in open systems with a view to developing new conceptual approaches to scattering theory. Efficient schemes to obtain scattering matrices from mean-field Hamiltonians are developed and these are implemented in new numerical codes. The relationship between the phase of S-matrix elements and Wigner delay times is also elucidated.I consider the scattering problem in a tight-binding lattice, as a simple way to understand the relation between M-functions and Greens functions and to investigate the connectivity dependence of Wigner delay times. To analyse delay times in bipartite lattices, tight binding calculations are used and a new computer code is developed to verify analytical predictions. In particular, Green’s functions and a mid-gap theory are used to calculate Wigner delay times for different connectivities in graphene like molecules. One interesting and counterintuitive result is that in the weak coupling limit at the middle of HOMO and LUMO gap, the Wigner delay time does not depend on the distance between the connections to external reservoirs.

AB - This thesis addresses the question of the time spent by a transmitted wave packet within a scattering region. The study involves mathematical aspects of solving the Schrodinger equation in open systems with a view to developing new conceptual approaches to scattering theory. Efficient schemes to obtain scattering matrices from mean-field Hamiltonians are developed and these are implemented in new numerical codes. The relationship between the phase of S-matrix elements and Wigner delay times is also elucidated.I consider the scattering problem in a tight-binding lattice, as a simple way to understand the relation between M-functions and Greens functions and to investigate the connectivity dependence of Wigner delay times. To analyse delay times in bipartite lattices, tight binding calculations are used and a new computer code is developed to verify analytical predictions. In particular, Green’s functions and a mid-gap theory are used to calculate Wigner delay times for different connectivities in graphene like molecules. One interesting and counterintuitive result is that in the weak coupling limit at the middle of HOMO and LUMO gap, the Wigner delay time does not depend on the distance between the connections to external reservoirs.

U2 - 10.17635/lancaster/thesis/192

DO - 10.17635/lancaster/thesis/192

M3 - Master's Thesis

PB - Lancaster University

ER -