عنوان

Spectral approach to transport problems in two-dimensional disordered lattices :

(Number (ISBN

3030022129

(Number (ISBN

9783030022129

Erroneous ISBN

3030022110

Erroneous ISBN

9783030022112

Title Proper

Spectral approach to transport problems in two-dimensional disordered lattices :

General Material Designation

[Book]

Other Title Information

physical interpretation and applications /

First Statement of Responsibility

Evdokiya Georgieva Kostadinova.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xiii, 107 pages) :

Other Physical Details

illustrations (some color)

Series Title

Springer theses,

ISSN of Series

2190-5053

Text of Note

"Doctoral thesis accepted by Baylor University, Waco, Texas, USA."

Text of Note

Intro; Supervisorś Foreword; Acknowledgments; Contents; Chapter 1: Introduction; 1.1 Formulation of the Transport Problem; 1.2 Nature of Disorder; 1.3 Relevance to Physical Systems; Bibliography; Chapter 2: Theoretical Background; 2.1 Localization Criteria; 2.2 Anderson Model; 2.3 Edwards and Thouless Model; 2.4 Scaling Theory; Bibliography; Chapter 3: Spectral Approach; 3.1 Essence of the Spectral Method; 3.1.1 Cyclic Subspaces and Equivalence Classes; 3.1.2 Spectral Decomposition of Normal Operators; 3.1.3 Extended States Conjecture and the Distance Formula

Text of Note

3.2 Simplified Numerical Model (``Toy Model)́́3.2.1 Application to the Discrete Random Schrödinger Operator; 3.2.2 Preliminary Results in 2D and 3D; 3.3 Physical Interpretation; 3.3.1 Band Structure and the Spectrum of the Hamiltonian; 3.3.2 Bounded Operators and the Hilbert Space; 3.4 Scope and Limitations of the Spectral Analysis; Bibliography; Chapter 4: Delocalization in 2D Lattices of Various Geometries; 4.1 Transport in the Honeycomb, Triangular, and Square Lattices; 4.2 Orthogonality Check; 4.3 Equation Fitting; 4.4 Cluster Analysis

Text of Note

4.5 Comparison Between the Honeycomb and the Triangular LatticesBibliography; Chapter 5: Transport in the Two-Dimensional Honeycomb Lattice with Substitutional Disorder; 5.1 Discrete Percolation; 5.2 Formulation of the Transport Problem; 5.2.1 Binary Alloy Model of Doping; 5.2.2 Quantum Percolation Problem; 5.2.3 Relation Between Quantum Percolation and Anderson Localization; 5.3 Distribution of Variables; 5.4 2D Honeycomb Lattice with Substitutional Disorder; Bibliography; Chapter 6: Transport in 2D Complex Plasma Crystals; 6.1 Complex Plasma Preliminaries

Text of Note

6.2 Two-Dimensional Dust Crystal Analogue6.3 Transport in the Classical Regime; 6.4 Numerical Simulations of Dust Particle Dynamics; 6.4.1 Dust Crystal Formation and Defect Types; 6.4.2 Crystal Perturbation; 6.5 Spectral Analysis; Bibliography; Chapter 7: Conclusions; Bibliography; Appendix A: Basic Materials Science Terms; Comparison Between Fermi Energy and Fermi Level; Appendix B: Mathematical Preliminaries; Kindergarten Math; Measure Theory; Point-Set Topology; Group Theory; Probability Theory; Curriculum Vitae

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Text of Note

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.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030022129

Title

Spectral approach to transport problems in two-dimensional disordered lattices.

International Standard Book Number

9783030022112

Lattice dynamics.

Nanoelectronics.

Lattice dynamics.

Nanoelectronics.

PHF

PHF

SCI077000

Number

Edition

Class number

Kostadinova, Evdokiya Georgieva

Date of Transaction

20200823073940.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y