We calculate the dielectric response of free-standing and supported two-dimensional layers of polarizable entities, such as metallic particles or adsorbed molecules. We take into account dipole-dipole and the image interaction and investigate the effects of disorder within a two-dimensional renormalized polarizability theory. The behavior of the resonances arising from both the single particle’s and the substrate’s surface plasmon is studied.

We develop a simple transfer-matrix formalism in order to obtain the dispersion relation of the electromagnetic normal modes of an infinite insulator-metal (or highly doped semiconductor) superlattice, taking into account the presence of plasma waves, spatial dispersion, and retardation. We also calculate the p-polarized reflectance and give analytical expressions for the surface impedance, reflection amplitude, and the dispersion relation of the surface modes of a semi-infinite superlattice. We find resonant features corresponding to the propagation of guided plasma waves in the metal layers coupled by transverse fields in the insulating layers. This coupling also yields new bulk modes in regions where propagation would not be allowed without spatial dispersion.

We carry out a detailed variational calculation of the binding energies of hydrogenic impurities in a cubic quantum box as a function of both the impurity position and an applied electric field. It is found that the binding energy of the impurities is highly dependent on the impurity position, and the electric field splits the energy of impurities on points of the box which are equivalent in the absence of the electric field. When the impurity is located at the upper half of the cube and the field pushes the particle downwards, then the binding energy decreases, whereas the Stark shift exhibits a minimum.

We discuss the existence of electromagnetic Stark ladder in some optic systems by studying the propagation of light. The transmission coefficient is calculated by means of the transfer-matrix method. It is shown that although the transfer matrix is different from the quantum case it can give, in some particular configurations, a Stark-ladder resonance structure similar to the one observed in quantum systems. The relation between these resonances and a Fabry-Perot-like interference is discussed. Consideration is given to the observability of these ladders in the laboratory.

The electron-hole interaction plays an important role in the optical spectra of semiconductors, not only in bound excitons in the energy-gap region, but also in the continuum. In particular, it affects the strength of the two major peaks in the absorption spectra of semiconductors of diamond and zinc-blende structures. A simple model is made to account for the band-structure effects. The Bethe-Salpeter equation containing the electron-hole interaction effect is solved to yield the absorption spectra for Si and Ge. A physical explanation of how the excitonic effects correct the strength of the $E_1$ and $E_2$ peaks in the right direction shows that our conclusions can be generalized to the III-V and II-VI compounds.

The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player’s advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is 0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player’s advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.