Spectral approach to transport problems in two-dimensional disordered lattices : physical interpretation and applications /: physical interpretation and applications. (2018)
- Record Type:
- Book
- Title:
- Spectral approach to transport problems in two-dimensional disordered lattices : physical interpretation and applications /: physical interpretation and applications. (2018)
- Main Title:
- Spectral approach to transport problems in two-dimensional disordered lattices : physical interpretation and applications
- Further Information:
- Note: Evdokiya Georgieva Kostadinova.
- Authors:
- Kostadinova, Evdokiya Georgieva
- Contents:
- 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 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 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; 5.3Intro; 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 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 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 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 … (more)
- Publisher Details:
- Cham, Switzerland : Springer
- Publication Date:
- 2018
- Extent:
- 1 online resource (xiii, 107 pages), illustrations (some color)
- Subjects:
- 530.4/11
Lattice dynamics
Nanoelectronics
Electronic books - Languages:
- English
- ISBNs:
- 9783030022129
3030022129 - Related ISBNs:
- 9783030022112
3030022110 - Notes:
- Note: Online resource; title from PDF title page (SpringerLink, viewed December 21, 2018).
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.381205
- Ingest File:
- 02_369.xml