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Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices

Physical Interpretation and Applications

  • Book
  • © 2018

Overview

Authors:
  1. Evdokiya Georgieva Kostadinova

    1. Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, USA

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  • Nominated as an outstanding PhD thesis by Baylor University
  • Gives an accessible introduction to Anderson-type transport problems
  • Presents an innovative spectral approach to wave propagation in two dimensional systems
  • Develops applications to 2D disordered complex plasma crystals

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Evdokiya Georgieva Kostadinova
    Pages 1-12

  3. Theoretical Background

    • Evdokiya Georgieva Kostadinova
    Pages 13-25

  4. Spectral Approach

    • Evdokiya Georgieva Kostadinova
    Pages 27-41

  5. Delocalization in 2D Lattices of Various Geometries

    • Evdokiya Georgieva Kostadinova
    Pages 43-53

  6. Transport in the Two-Dimensional Honeycomb Lattice with Substitutional Disorder

    • Evdokiya Georgieva Kostadinova
    Pages 55-72

  7. Transport in 2D Complex Plasma Crystals

    • Evdokiya Georgieva Kostadinova
    Pages 73-86

  8. Conclusions

    • Evdokiya Georgieva Kostadinova
    Pages 87-90

  9. Back Matter

    Pages 91-107
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Keywords

About this book

This book introduces the spectral approach to transport problems in infinite disordered systems characterized by Anderson-type Hamiltonians. The spectral approach determines (with probability one) the existence of extended states for nonzero disorder in infinite lattices of any dimension and geometry. Here, the author focuses on the critical 2D case, where previous numerical and experimental results have shown disagreement with theory. Not being based on scaling theory, the proposed method avoids issues related to boundary conditions and provides an alternative approach to transport problems where interaction with various types of disorder is considered.


Beginning with a general overview of Anderson-type transport problems and their relevance to physical systems, it goes on to discuss in more detail the most relevant theoretical, numerical, and experimental developments in this field of research. The mathematical formulation of the innovative spectral approach is introduced together with a physical interpretation and discussion of its applicability to physical systems, followed by a numerical study of delocalization in the 2D disordered honeycomb, triangular, and square lattices. Transport in the 2D honeycomb lattice with substitutional disorder is investigated employing a spectral analysis of the quantum percolation problem. Next, the applicability of the method is extended to the classical regime, with an examination of diffusion of lattice waves in 2D disordered complex plasma crystals, along with discussion of proposed future developments in the study of complex transport problems using spectral theory.


Authors and Affiliations

  • Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, USA

    Evdokiya Georgieva Kostadinova

About the author

Evdokiya Georgieva Kostadinova is a research assistant professor in the Center for Astrophysics, Space Physics & Engineering Research at Baylor University. She received her PhD from Baylor University in 2017. 

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