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Springer Theses

Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices

Physical Interpretation and Applications

Authors: Kostadinova, Evdokiya Georgieva

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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
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-030-02212-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-02211-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

About the authors

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. 

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-030-02212-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-02211-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices
Book Subtitle
Physical Interpretation and Applications
Authors
Series Title
Springer Theses
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-02212-9
DOI
10.1007/978-3-030-02212-9
Hardcover ISBN
978-3-030-02211-2
Series ISSN
2190-5053
Edition Number
1
Number of Pages
XIII, 107
Number of Illustrations
3 b/w illustrations, 36 illustrations in colour
Topics