Minute Metallic Particles in an Electromagnetic Field

We consider some properties of metallic particles with dimensions so small that the spectrum of the electronic excitations becomes discrete. The existence of microscopic roughnesses on the particle surfaces makes it impossible to calculate the detailed level distribution in the spectrum of each individual particle. At the same time, the mean level density is still determined by the macroscopic characteristics of the metal. This circumstance allows us to describe the level distribution statistically, in a manner similar to that employed in nuclear physics to find the distribution of the highly excited levels of the atomic nucleus. The formulas obtained for the electric polarizability in a high-frequency field, especially the part of the polarizability responsible for the absorption, contain explicitly the binary correlation function introduced in Dyson's well-known papers. It is shown that all three types of level statistics proposed by Dyson are realized in the objects under study under different conditions. It therefore becomes possible to observe in the level scheme of a random system a long-range order that leads to strong oscillations of the absorption when the field frequency is varied. Formulas are also obtained for the specific heat and for the paramagnetic-resonance intensity in minute metallic particles. The possibility of experimentally observing the phenomena in question is discussed.