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Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices

Physical Interpretation and Applications

  • Evdokiya Georgieva┬áKostadinova

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Evdokiya Georgieva Kostadinova
    Pages 1-12
  3. Evdokiya Georgieva Kostadinova
    Pages 13-25
  4. Evdokiya Georgieva Kostadinova
    Pages 27-41
  5. Evdokiya Georgieva Kostadinova
    Pages 43-53
  6. Evdokiya Georgieva Kostadinova
    Pages 73-86
  7. Evdokiya Georgieva Kostadinova
    Pages 87-90
  8. Back Matter
    Pages 91-107

About this book

Introduction

This thesis 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.

Keywords

transport in infinite disordered systems Anderson-type Hamiltonians delocalization in 2D lattices spectral analysis quantum percolation problem 2D disordered complex plasma cystals complex transport problems anderson localization discrete random Schroedinger operator 2D disordered lattice Quantum percolation Anomalous transport Scaling of Thouless model Substitutional disorder

Authors and affiliations

  • Evdokiya Georgieva┬áKostadinova
    • 1
  1. 1.Center for Astrophysics, Space Physics and Engineering ResearchBaylor UniversityWacoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02212-9
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-030-02211-2
  • Online ISBN 978-3-030-02212-9
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site
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