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Table of Contents
Intro; Preface; Contents; Acronyms; Symbols; 1 Introduction; References; Part I Background Material; 2 Electromagnetism; 2.1 Maxwell's Equations; 2.2 Unit System; 2.3 Constitutive Relations; 2.4 Potentials; 2.5 Boundary Conditions; 2.6 The Fresnel Equations; 2.6.1 Reflection and Transmission for Normal Incidence; 2.6.2 Oblique Incidence; 2.6.3 Anisotropic Media; 2.7 Special Considerations for 2D Sheets; 2.7.1 Fourier Transforms of a Special Function; 2.7.2 Method of Images; 2.7.3 Screening Functions in a 2D System; 2.8 Fields from a Time-Dependent Electric or Magnetic Dipole; References.
3 Complex Analysis3.1 Analytic Functions; 3.2 Laurent Expansion and Residues; 3.3 Contour Integration in the Complex Plane; 3.3.1 Integration Around a Pole; 3.3.2 Argument Principle and Its Extension; 3.4 Analytic Properties of Response Functions; 3.4.1 Kramers Kronig Dispersion Relations; Reference; 4 Statistical Physics; 4.1 Thermodynamic Potentials and Legendre Transformations; 4.2 Distribution Functions; 4.3 Internal Energy and Helmholtz Energy for System of Mass-Less Bosons; Reference; 5 Electromagnetic Normal Modes; 5.1 Normal Modes and Their Properties.
5.1.1 The Quantum Mechanical Harmonic Oscillator5.1.2 Classical Versus Quantum Systems; 5.2 Interaction from Normal Modes; 5.3 Different Mode Types; 5.3.1 Vacuum Modes; 5.3.2 Bulk Modes; 5.3.3 Surface Modes; 5.4 Modes for a Gap Between Two Half Spaces; 5.4.1 Transverse Magnetic Modes; 5.4.2 Transverse Electric Modes; 5.4.3 Modes in Non-retarded Treatment; References; 6 Different Approaches; 6.1 Summation of Pair Interactions; 6.2 Interactions Between Objects at Small Separations: The Proximity Force Approximation; 6.2.1 General Expression for Half Spaces, Cylinders and Spheres.
6.3 Many-Body Approach in Non-Retarded Treatment6.4 Many-Body Approach in Fully Retarded Treatment; 6.5 Brief Compilation of Methods or Approaches; References; 7 General Method to Find the Normal Modes in Layered Structures; 7.1 The Scheme; References; Part II Non-Retarded Formalism: van der Waals; 8 Van der Waals Force; 8.1 Equation of State for Ideal Gas; 8.1.1 2D Version; 8.2 Equation of State for Non-ideal Gas; 8.2.1 2D Version; 8.3 Van der Waals Force Between Two Atoms; 8.3.1 Zero Temperature; 8.3.2 Finite Temperature; References; 9 Van der Waals Interaction in Planar Structures.
9.1 Adapting the General Method of Chap. 7 to Planar Structures and to the Neglect of Retardation9.2 Basic Structure Elements; 9.2.1 Single Planar Interface; 9.2.2 Planar Layer; 9.2.3 2D Planar Film; 9.2.4 Thin Planar Diluted Gas Film; 9.3 Two Half Spaces; 9.3.1 Interaction Between Two Gold Half Spaces; 9.4 Two Slabs; 9.4.1 Interaction Between Two Gold Slabs; 9.5 Two 2D Films; 9.5.1 Interaction Between Two Graphene Sheets; 9.5.2 Interaction Between Two 2D Metal Films; 9.6 Film-Wall; 9.6.1 Interaction Between Graphene and an Au-Wall; 9.6.2 Interaction Between a 2D Metal Film and an Au-Wall.
3 Complex Analysis3.1 Analytic Functions; 3.2 Laurent Expansion and Residues; 3.3 Contour Integration in the Complex Plane; 3.3.1 Integration Around a Pole; 3.3.2 Argument Principle and Its Extension; 3.4 Analytic Properties of Response Functions; 3.4.1 Kramers Kronig Dispersion Relations; Reference; 4 Statistical Physics; 4.1 Thermodynamic Potentials and Legendre Transformations; 4.2 Distribution Functions; 4.3 Internal Energy and Helmholtz Energy for System of Mass-Less Bosons; Reference; 5 Electromagnetic Normal Modes; 5.1 Normal Modes and Their Properties.
5.1.1 The Quantum Mechanical Harmonic Oscillator5.1.2 Classical Versus Quantum Systems; 5.2 Interaction from Normal Modes; 5.3 Different Mode Types; 5.3.1 Vacuum Modes; 5.3.2 Bulk Modes; 5.3.3 Surface Modes; 5.4 Modes for a Gap Between Two Half Spaces; 5.4.1 Transverse Magnetic Modes; 5.4.2 Transverse Electric Modes; 5.4.3 Modes in Non-retarded Treatment; References; 6 Different Approaches; 6.1 Summation of Pair Interactions; 6.2 Interactions Between Objects at Small Separations: The Proximity Force Approximation; 6.2.1 General Expression for Half Spaces, Cylinders and Spheres.
6.3 Many-Body Approach in Non-Retarded Treatment6.4 Many-Body Approach in Fully Retarded Treatment; 6.5 Brief Compilation of Methods or Approaches; References; 7 General Method to Find the Normal Modes in Layered Structures; 7.1 The Scheme; References; Part II Non-Retarded Formalism: van der Waals; 8 Van der Waals Force; 8.1 Equation of State for Ideal Gas; 8.1.1 2D Version; 8.2 Equation of State for Non-ideal Gas; 8.2.1 2D Version; 8.3 Van der Waals Force Between Two Atoms; 8.3.1 Zero Temperature; 8.3.2 Finite Temperature; References; 9 Van der Waals Interaction in Planar Structures.
9.1 Adapting the General Method of Chap. 7 to Planar Structures and to the Neglect of Retardation9.2 Basic Structure Elements; 9.2.1 Single Planar Interface; 9.2.2 Planar Layer; 9.2.3 2D Planar Film; 9.2.4 Thin Planar Diluted Gas Film; 9.3 Two Half Spaces; 9.3.1 Interaction Between Two Gold Half Spaces; 9.4 Two Slabs; 9.4.1 Interaction Between Two Gold Slabs; 9.5 Two 2D Films; 9.5.1 Interaction Between Two Graphene Sheets; 9.5.2 Interaction Between Two 2D Metal Films; 9.6 Film-Wall; 9.6.1 Interaction Between Graphene and an Au-Wall; 9.6.2 Interaction Between a 2D Metal Film and an Au-Wall.