L.G. Suttorp

Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics

The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-Schwinger equation for the electric field operator plays a central role. The equation describes atoms as point sources and point scatterers for light. First, single-atom properties are calculated such as position-dependent spontaneous-emission rates as well as differential cross sections for elastic scattering and for resonance fluorescence. Secondly, multiatom processes are studied. It is shown that the medium modifies both the resonant and the static parts of the dipole-dipole interactions. These interatomic interactions may cause the atoms to scatter and emit light cooperatively. Unlike in free space, differences in position-dependent emission rates and radiative line shifts influence cooperative decay in the dielectric. As a generic example, it is shown that near a partially reflecting plane there is a sharp transition from two-atom superradiance to single-atom emission as the atomic positions are varied.

Field quantization in inhomogeneous absorptive dielectrics

The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.

The relativistic energy-momentum tensor in polarized media: VII. Discussion of the results in connexion with previous work

Abstract The literature on the relativistic energy-momentum tensor in polarized media falls apart in treatments based on microscopic first principles and considerations starting from macroscopic postulates. Only papers of the first category, such as Lorentzs and Einstein-Laubs, can be considered as derivations, whereas treatments of the second category, such as Minkowskis and Abrahams, based on ad hoc assumptions, do not give unique results.

The relativistic energy-momentum tensor in polarized media: III. Statistical theory of the energy-momentum laws☆

Abstract From the atomic conservation laws of energy-momentum the corresponding macroscopic laws are derived with the help of a covariant averaging procedure. The total energy-momentum tensor is found as a statistical expression in terms of atomic quantities. It may be split into a field part T αβ (⨍) (α, β = 0, 1, 2, 3) containing the macroscopic fields and polarizations, which in the rest frame reads: T αβ (⨍) = 1 2 E 2 + 1 2 B 2 (E ∧ H) i (E∧H) i −E i D j −H i B j +( 1 2 E 2 + 1 2 B 2 −M⋅B)g ij (i,j =1,2,3) and a material part Tαβ(m) which forms the relativistic generalization of the usual energy and momentum expressions.

Fano diagonalization of a polariton model for an inhomogeneous absorptive dielectric

The Hamiltonian of a polariton model for an inhomogeneous linear absorptive dielectric is diagonalized by means of Fanos diagonalization method. The creation and annihilation operators for the independent normal modes are explicitly found as linear combinations of the canonical operators. The coefficients in these combinations depend on the tensorial Green function that governs the propagation of electromagnetic waves through the dielectric. The time-dependent electromagnetic fields in the Heisenberg picture are given in terms of the diagonalizing operators. These results justify the phenomenological quantization of the electromagnetic field in an absorptive dielectric.

Equilibrium properties of a multi-component ionic mixture

Equilibrium statistical methods are used to derive sum rules for two- and three-particle correlation functions of a multi-component ionic mixture. Some of these rules are general consequences of the electrostatic character of the interaction, whereas others depend on specific thermodynamic properties of the system. The first group of rules follows from the BBGKY hierarchy and a clustering hypothesis for Ursell functions. The sum rules of the second group are obtained by describing the system with the help of a restricted grand-canonical ensemble in which the particle numbers of the various components in the mixture fluctuate under the condition that the total charge in the system remains constant.

Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion

A quantum damped-polariton model is constructed for an inhomogeneous anisotropic linear dielectric with arbitrary dispersion in space and time. The model Hamiltonian is completely diagonalized by determining the creation and annihilation operators for the fundamental polariton modes as specific linear combinations of the basic dynamical variables. Explicit expressions are derived for the time-dependent operators describing the electromagnetic field, the dielectric polarization and the noise term in the latter. It is shown how to identify bath variables that generate the dissipative dynamics of the medium.

Covariant derivation of the Maxwell equations: Multipole expansion of the polarization tensor to all orders

Abstract The Maxwell equations are derived in covariant manner from the microscopic equations for the electromagnetic field in the presence of point charges. The polarization tensor is given as an expansion to all orders in the atomic electromagnetic moments, defined in atomic rest frames.

Multipole expansion of the retarded interatomic dispersion energy: derivation from quantum electrodynamics

Abstract The multipole expansion of the retarded dispersion energy of two atoms in non-degenerate ground states is derived. The result shows that multipoles of different order may give rise to dispersion energies varying in the same way for large interatomic separations.

The relativistic energy-momentum tensor in polarized media: II. The angular momentum laws and the symmetry of the energy-momentum tensor

Abstract The angular momentum balance of matter in an electromagnetic field on the atomic level is derived from microscopic theory. As a consequence an energy-momentum tensor can be constructed, which is completely symmetrical. Both its material and field parts are given explicitly in terms of the atomic parameters.