Non-Relativistic QED Theory of the van der Waals Dispersion Interaction

Non-Relativistic QED


Author:
Akbar Salam
Published in: Springer International Publishing
Release Year: 2016
ISBN: 978-3-319-45606-5
Pages: 113
Edition: First Edition
File Size: 2 MB
File Type: pdf
Language: English



Description of Non-Relativistic QED


Non-Relativistic QED, Why it may reasonably be asked, write on the subject of dispersion forces and add to the already existing high-quality literature dealing with molecular QED theory? A complete answer to the question emerges after consideration of several diverse aspects. The dispersion interaction occurs between all material particles from the atomic scale upward and is a purely quantum mechanical phenomenon. 
Employing a quantized electromagnetic field–matter coupling approach allows for its rigorous calculation, along with an elementary understanding of the origin and manifestation of this fundamental interaction. Fluctuations of the ground state charge and current densities of the source and the vacuum field interact via the propagation of virtual photons—by definition unobservable quanta of light, resulting in an attractive force between atoms and molecules. 
The ubiquitous nature of the dispersion interaction means that it impacts a wide range of scientific disciplines and subareas. An opportunity therefore presents itself to bring the pioneering work of Casimir and Polder to an even broader audience, one who might ordinarily only be well versed with the London dispersion formula, by exposing them to the eponymous potential associated with the two aforementioned Dutch physicists, and the extension of their result to related applications involving contributions from higher multipole moment terms and/or coupling between three particles. 
This topic is also timely from the point of view that lately there has been renewed interest in a variety of van der Waals dominated processes, ranging from the physisorption of atoms and small molecules on semiconductor surfaces to the hanging and climbing ability of geckos. These and many other problems continue to be studied experimentally and theoretically. In this second category, advances have occurred at both the microscopic and the macroscopic levels of description, frequently within the framework of QED.

Content of Non-Relativistic QED


1 Introduction.............................................. 1
1.1 The Inter-Particle Potential ............................... 1
1.2 The Born-Oppenheimer Approximation ..................... 2
1.3 The Interaction Energy at Long-Range ...................... 3
1.4 Electrostatic Energy .................................... 4
1.5 Induction Energy ...................................... 5
1.6 Dispersion Energy ..................................... 6
1.7 Photons: Real and Virtual Light Quanta ..................... 8
1.8 Dispersion Forces Between Macroscopic Objects.............. 9
1.9 Different Physical Ways of Understanding the Dispersion
Interaction Between Atoms and Molecules................... 11
References................................................ 14
2 Non-relativistic QED ....................................... 17
2.1 Classical Mechanics and Electrodynamics ................... 17
2.2 Lagrangian for a Charged Particle Coupled to Electromagnetic
Radiation ............................................ 21
2.3 Minimal-Coupling QED Hamiltonian ....................... 25
2.4 Multipolar-Coupling QED Hamiltonian ..................... 29
2.5 Perturbative Solution to the QED Hamiltonian ................ 35
References................................................ 36
3 Dispersion Interaction Between Two Atoms or Molecules ......... 39
3.1 Casimir-Polder Potential: Minimal-Coupling Calculation ........ 39
3.2 Casimir-Polder Energy Shift: Multipolar Formalism
Calculation ........................................... 45
3.3 Asymptotically Limiting Forms ........................... 49
3.4 Correlation of Fluctuating Electric Dipoles................... 52
References................................................ 55
4 Inclusion of Higher Multipole Moments ....................... 57
4.1 Introduction .......................................... 57
4.2 Generalised Dispersion Energy Shift for Molecules
with Arbitrary Electric Multipoles ......................... 58
4.3 Electric Dipole-Quadrupole Dispersion Potential .............. 61
4.4 Electric Quadrupole-Quadrupole Interaction Energy ............ 63
4.5 Electric Dipole-Octupole Energy Shift ...................... 64
4.6 Electric Dipole-Magnetic Dipole Potential ................... 66
4.7 Inclusion of Diamagnetic Coupling ........................ 68
4.8 Discriminatory Dispersion Potential ........................ 70
References................................................ 73
5 van der Waals Dispersion Force Between Three Atoms or
Molecules ................................................ 75
5.1 Introduction .......................................... 75
5.2 Two-Photon Coupling: The Craig-Power Hamiltonian .......... 76
5.3 Triple Dipole Dispersion Potential ......................... 78
5.4 Far- and Near-Zone Limits............................... 82
5.5 Equilateral Triangle Geometry ............................ 84
5.6 Collinear Arrangement .................................. 85
5.7 Right-Angled Triangle Configuration ....................... 86
References................................................ 87
6 Three-Body Dispersion Energy Shift: Contributions
from Higher Electric Multipoles.............................. 89
6.1 Introduction .......................................... 89
6.2 Generalised Three-Body Dispersion Potential................. 90
6.3 Dipole-Dipole-Quadrupole Potential ........................ 92
6.4 Dipole-Quadrupole-Quadrupole Dispersion Energy Shift ........ 95
6.5 Dipole-Dipole-Octupole Dispersion Potential ................. 98
References................................................ 101
Index ...................................................... 103
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