THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

Thank you for downloading introduction to electrodynamics. Maybe you have knowledge that, people have look numerous times for their chosen books like this introduction to electrodynamics, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they juggled with some malicious bugs inside their computer. introduction to electrodynamics is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the introduction to electrodynamics is universally compatible with any devices to read.

Introduction To Electrodynamics

The quantum-confined Stark effect in single cadmium selenide (CdSe) nanocrystallite quantum dots was studied. The electric field dependence of the single-dot spectrum is characterized by a highly polarizable excited state (∼10 5 cubic angstroms, compared to typical molecular values of order 10 to 100 cubic angstroms), in the presence of randomly oriented local electric fields that change over time. These local fields result in spontaneous spectral diffusion and contribute to ensemble inhomogeneous broadening. Stark shifts of the lowest excited state more than two orders of magnitude larger than the linewidth were observed, suggesting the potential use of these dots in electro-optic modulation devices.

Quantum Confined Stark Effect in Single CdSe Nanocrystallite Quantum Dots

Intermolecular bonds are weak compared to covalent bonds, but they are strong enough to influence the properties of large molecular systems. In this work, we investigate how strong light-matter coupling inside an optical cavity can modify these intermolecular forces. We perform a detailed comparison between currently available ab initio electron-photon methodologies. The electromagnetic field inside the cavity can modulate the ground state properties of weakly bound complexes. Controlling the field polarization, the interactions can be stabilized or destabilized, and electron densities, dipole moments, and polarizabilities can be altered. We demonstrate that electron-photon correlation is fundamental to describe intermolecular interactions in strong light-matter coupling. This work proposes optical cavities as a novel tool to manipulate and control ground state properties, solvent effects, and intermolecular interactions for molecules and materials.

Intermolecular interactions in optical cavities: an ab initio QED study

Motivated by recent experiments, the laser-induced alignment-and-orientation (A&O) dynamics of the prolate symmetric top CH3 X (X = F, Cl, Br, I) molecules is investigated, with particular emphasis on the effect of halogen substitution on the rotational constants, dipole moments, and polarizabilities of these species, as these quantities determine the A&O dynamics. Insight into possible control schemes for preferred A&O dynamics of halogenated molecules and best practices for A&O simulations are provided, as well. It is shown that for accurate A&O -dynamics simulations it is necessary to employ large basis sets and high levels of electron correlation when computing the rotational constants, dipole moments, and polarizabilities. The benchmark-quality values of these molecular parameters, corresponding to the equilibrium, as well as the vibrationally averaged structures are obtained with the help of the focal-point analysis (FPA) technique and explicit electronic-structure computations utilizing the gold-standard CCSD(T) approach, basis sets up to quintuple-zeta quality, core-correlation contributions and, in particular, relativistic effects for CH3 Br and CH3 I. It is shown that the different A&O behavior of the CH3 X molecules in the optical regime is mostly caused by the differences in their polarizability anisotropy, in other terms, the size of the halogen atom. In contrast, the A&O dynamics of the CH3 X series induced by an intense few-cycle THz pulse is mostly governed by changes in the rotational constants, due to the similar dipole moments of the CH3 X molecules. The A&O dynamics is most sensitive to the B rotational constant: even the difference between its equilibrium and vibrationally-averaged values results in noticeably different A&O dynamics. The contribution of rotational states having different symmetry, weighted by nuclear-spin statistics, to the A&O dynamics is also studied. 

A quantum‐chemical perspective on the laser‐induced alignment and orientation dynamics of the <scp>CH</scp> <sub>3</sub> X (X = F, Cl, Br, I) molecules

Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, $\alpha$, rely on different scaling laws $\alpha \propto$ $R^3$, $R^4$, or $R^7$, for various definitions of the system radius $R$. Here, we consider a range of atom-like quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law $\alpha = C (4 \mu q^2/\hbar^2)L^4$, where $\mu$ and $q$ are the (effective) particle mass and charge, $C$ is a dimensionless ratio between effective excitation energies, and the characteristic length $L$ is defined via the $\mathcal{L}^2$-norm of the position operator. The applicability of this unified formula is demonstrated by accurately predicting the dipole polarizability of 36 atoms and 1641 small organic~molecules.

Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems

We employ various quantum-mechanical approaches for studying the impact of electric fields on both nonretarded and retarded noncovalent interactions between atoms or molecules. To this end, we apply perturbative and non-perturbative methods within the frameworks of quantum mechanics (QM) as well as quantum electrodynamics (QED). In addition, to provide a transparent physical picture of the different types of resulting interactions, we employ a stochastic electrodynamic approach based on the zero-point fluctuating field. Atomic response properties are described via harmonic Drude oscillators - an efficient model system that permits an analytical solution and has been convincingly shown to yield accurate results when modeling non-retarded intermolecular interactions. The obtained intermolecular energy contributions are classified as field-induced (FI) electrostatics, FI polarization, and dispersion interactions. The interplay between these three types of interactions enables the manipulation of molecular dimer conformations by applying transversal or longitudinal electric fields along the intermolecular axis. Our framework combining four complementary theoretical approaches paves the way toward a systematic description and improved understanding of molecular interactions when molecules are subject to both external and vacuum fields.

Comprehensive Quantum Framework for Describing Retarded and Non-Retarded Molecular Interactions in External Electric Fields

We study the interaction between two neutral atoms or molecules subject to a uniform static electric field, using quantum mechanics (QM) and quantum electrodynamics (QED) applied to coupled harmonic Drude oscillators. Our focus is to understand the interplay between dispersion interactions and field-induced electrostatics and polarization in both retarded and non-retarded regimes. We present an exact solution for two coupled oscillators using QM and Rayleigh-Schr\"odinger perturbation theory, demonstrating that the external field controls the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by QED and rationalized by stochastic electrodynamics, our analysis shows that field-induced electrostatics and polarization terms remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded QM description, in contrast to a recent work. Our framework combining four complementary theoretical approaches paves the way to a systematic description and enhanced understanding of molecular interactions under the combined action of external and vacuum fields.

Mohammad Reza Karimpour

Papers

Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems

Comprehensive Quantum Framework for Describing Retarded and Non-Retarded Molecular Interactions in External Electric Fields

Molecular Interactions Induced by an Electric Field in Quantum Mechanics and Quantum Electrodynamics