Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices

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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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.

• 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
• partial differential equations

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

  Evdokiya Georgieva Kostadinova

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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