The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and the second part of this dissertation aims at this important task. This dissertation proves that the adoption of a master equation approach, and so of probabilistic as well as dynamical argument yields a satisfactory solution of the problem, as shown in a work by the candidate already published. At the same time, this dissertation shows that the foundation of Levy statistics is compatible with ordinary statistical mechanics and thermodynamics. The problem of the connection with the Kolmogorov-Sinai entropy is a delicate problem that, however, can be successfully solved. The derivation from a microscopic Liouville-like approach based on densities, however, is shown to be impossible. …

This dissertation addresses the delicate problem of establishing the statistical mechanical foundation of complex processes. These processes are characterized by a delicate balance of randomness and order, and a correct paradigm for them seems to be the concept of sporadic randomness. First of all, we have studied if it is possible to establish a foundation of these processes on the basis of a generalized version of thermodynamics, of non-extensive nature. A detailed account of this attempt is reported in Ignaccolo and Grigolini (2001), which shows that this approach leads to inconsistencies. It is shown that there is no need to generalize the Kolmogorov-Sinai entropy by means of a non-extensive indicator, and that the anomaly of these processes does not rest on their non-extensive nature, but rather in the fact that the process of transition from dynamics to thermodynamics, this being still extensive, occurs in an exceptionally extended time scale. Even, when the invariant distribution exists, the time necessary to reach the thermodynamic scaling regime is infinite. In the case where no invariant distribution exists, the complex system lives forever in a condition intermediate between dynamics and thermodynamics. This discovery has made it possible to create a new method of analysis …

Multilayer structures of AlxIn1-xAsySb1-y/GaSb (0.37 £ x £ 0.43, 0.50 £ y £ 0.52), grown by molecular beam epitaxy on GaSb (100) substrates were characterized using variable temperature Hall and Shubnikov-de Haas techniques. For nominally undoped structures both p and n-type conductivity was observed. The mobilities obtained were lower than those predicted by an interpolation method using the binary alloys; therefore, a detailed analysis of mobility versus temperature data was performed to extract the appropriate scattering mechanisms. For p-type samples, the dominant mechanism was ionized impurity scattering at low temperatures and polar optical phonon scattering at higher temperatures. For n-type samples, ionized impurity scattering was predominant at low temperatures, and electron-hole scattering dominated for both the intermediate and high temperature range. Analyses of the Shubnikov-de Haas data indicate the presence of 2-D carrier confinement consistent with energy subbands in GaAszSb1-z potential wells. Epilayers of GaAs1-xSbx (0.19<x<0.71), grown by MBE on semi-insulating GaAs with various substrate orientations, were studied by absorption measurements over the temperature range of 4-300 K. The various substrate orientations were chosen to induce different degrees of spontaneous atomic ordering. The temperature dependence of the energy gap (Eg) for each of these samples was modeled using three semi-empirical …

The unusually large hyperfine structure splittings in the 23P state of the 3He isotope is measured using electro-optic techniques with high precision laser spectroscopy. Originally designed to probe the fine structure of the 4He atom, this experimental setup along with special modifications I implemented to resolve certain 3He related issues has made possible new high precision hyperfine structure measurements. Discussed are the details of the experimental setup and the modifications, including in depth information necessary to consider while performing these measurements. The results of these hyperfine structure measurements give an order of magnitude improvement in precision over the best previously reported values.