ENGLISH

Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices: Physical Interpretation and Applications

By Evdokiya Georgieva Kostadinova

Book information

Publisher
Springer International Publishing
Year
2018
ISBN
978-3-030-02211-2, 978-3-030-02212-9
Language
english
Format
PDF
Filesize
3 MB (3237475 bytes)
Series
Springer Theses
Edition
1st ed.
Pages
XIII, 107\114
Time added
2019-01-12 07:35:39
Physics; Condensed Matter Physics; Mathematical Me

Description

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. Front Matter ....Pages i-xiii Introduction (Evdokiya Georgieva Kostadinova)....Pages 1-12 Theoretical Background (Evdokiya Georgieva Kostadinova)....Pages 13-25 Spectral Approach (Evdokiya Georgieva Kostadinova)....Pages 27-41 Delocalization in 2D Lattices of Various Geometries (Evdokiya Georgieva Kostadinova)....Pages 43-53 Transport in the Two-Dimensional Honeycomb Lattice with Substitutional Disorder (Evdokiya Georgieva Kostadinova)....Pages 55-72 Transport in 2D Complex Plasma Crystals (Evdokiya Georgieva Kostadinova)....Pages 73-86 Conclusions (Evdokiya Georgieva Kostadinova)....Pages 87-90 Back Matter ....Pages 91-107

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