We have studied the distribution of resonance widths $P\left(\Gamma \right)$ in one-, two-, and three-dimensional multiple light scattering systems. $P\left(\Gamma \right)$ should follow a universal power law $P\left(\Gamma \right)\sim {\Gamma }^{-1}$ in the localized regime as confirmed by extensive numerical calculations. This behavior can be interpreted as an unambiguous signature of exponential Anderson localization of light in open systems.

Universal properties of the spectra of certain matrices describing multiple elastic scattering of scalar waves from a collection of randomly distributed point-like objects are discovered. The elements of these matrices are equal to the free-space Green’s function calculated for the differences between positions of any pair of scatterers. A striking physical interpretation within Breit-Wigner’s model of the single scatterer is elaborated. Proximity resonances and Anderson localization are considered as two illustrative examples.

By performing extensive angle-resolved photoemission measurements using tunable linearly polarized synchrotron radiation with photon energies from 15 to 31 eV on high quality cleaved samples we have succeeded in experimentally mapping the occupied electronic bands of GaSe(0001) along all key symmetry directions. The experimental results are in very good agreement with state-of-the-art ab initio theoretical calculations. The data were analyzed assuming a direct transition model and final-state effects are discussed in the analysis of the normal-emission data. The off-normal emission spectra accurately reproduce the gaps in the calculated projected band structure. The azimuthal symmetry of the photocurrent revealed the polytype of the samples investigated.

A systematic approach to the localization of light waves in three-dimensional dielectric media is developed. A general definition of localization of electromagnetic waves is proposed and its consequences are elaborated. A significant amount of localization of the energy density of the electromagnetic field is predicted in finite systems of randomly distributed dielectric particles modeled by dipoles linearly coupled to the electric field of the incident wave. Although in this case it is not possible to achieve perfect localization, the predicted phenomenon is experimentally indistinguishable from a complete localization. Our approach is based directly on the Maxwell equations; the vector character of the electromagnetic waves is fully taken into account. The concepts presented in our previous paper [M. Rusek and A. Orłowski, Phys. Rev. E 51, R2763 (1995)] are now generalized to the three-dimensional case. Instead of using the Kirchhoff integral formula for scalar waves, we now analyze light scattering by pointlike dielectric particles as the special case of general considerations dealing with elastic scattering of electromagnetic waves by arbitrary localized charges and currents.

Exact solutions to many-body interacting systems of both bosonic and fermionic particles confined to harmonic potential in an arbitrary number of dimensions are given. Energy levels and their degeneracies for trapped identical particles interacting via harmonic forces are calculated. This specific form of the interaction allows for analytical solutions. The mutual interaction, attractive or repulsive, modifies significantly the properties of the considered system. For a large number of particles the interaction essentially results in a frequency shift. Statistical properties (e.g., microcanonical and grand canonical partition functions) as well as some illustrative, physically relevant examples are discussed. Our results give an unusual opportunity for further studies of interacting systems in the framework of the exactly soluble model.

Quantum-mechanical entropies of position and momentum operators in a given state are shown to be reasonable and sensitive measures for squeezing of quantum fluctuations. It is shown to be true not only for states having Gaussian wave functions but also for more general, both pure and mixed, quantum states. A simple proof that the squeezing exhibited by the variance is always accompanied by a corresponding entropy reduction below the entropy vacuum level is given. These results show that the information entropy is not only a theoretically satisfactory concept but can also be useful as a tool for more practical quantum-optics applications.