Based on a model Hamiltonian appropriate for the description of fermionic systems such as semiconductor lasers, we describe a natural asymptotic closure of the BBGKY hierarchy in complete analogy with that derived for classical weak turbulence. The main features of the interaction Hamiltonian are the inclusion of full Fermi statistics containing Pauli blocking and a simple, phenomenological, uniformly weak two particle interaction potential equivalent to the static screening approximation. The resulting asymytotic closure and quantum kinetic Boltzmann equation are derived in a self consistent manner without resorting to a priori statistical hypotheses or cumulant discard assumptions. We find a new class of solutions to the quantum kinetic equation which are analogous to the Kolmogorov spectra of hydrodynamics and classical weak turbulence. They involve finite fluxes of particles and energy across momentum space and are particularly relevant for describing the behavior of systems containing sources and sinks. We explore these solutions by using differential approximation to collision integral. We make a prima facie case that these finite flux solutions can be important in the context of semiconductor lasers. We show that semiconductor laser output efficiency can be improved by exciting these finite flux solutions. Numerical simulations of the semiconductor Maxwell Bloch equations support the claim.

In this thesis, we have systematically investigated the stability, surface dynamics, electronic transport, and growth of metal nanowires using a semiclassical free energy functional based on the mean-field interacting electron model, which is simple and general enough. In this model, the ionic degrees of freedom of the wire are modeled as an incompressible fluid, and the conducting electrons are treated as a Fermi gas confined within the wire with Dirichlet boundary conditions. In equilibrium, we prove that the electron-electron interaction is a second-order effect to the total grand canonical free energy, while the shell-correction to the noninteracting grand canonical free energy is a first-order effect. To leading order, the electron-electron interactions just renormalize the Weyl parameters, such as the average energy density, surface tension and mean curvature energy, but not the mesoscopic shell effect. This finding for open mesoscopic systems is a generalization of the well-known Strutinsky theorem for finite-Fermion systems. It is for this reason that self-consistent jellium calculations obtain essentially identical equilibrium mesoscopic effects as calculations based on the free-electron model. However, for systems out of equilibrium, the electron-electron interaction plays important roles. First of all, the Strutinsky theorem breaks down in the non-equilibrium case. Secondly, the gauge invariance condition is violated if the electron-electron interaction is not adequately included. We first derive a thermodynamic phase diagram for jellium nanowires, which predicts that cylindrical wires with certain "magic" conductance values are stable with respect to small perturbations up to remarkably high temperatures and high applied voltage. We have shown that Jahn-Teller-distorted wires can be stable. The derived sequence of stable cylindrical and elliptical geometries explains the experimentally observed shell and supershell structures for alkali metals. Highly deformed wires can explain additional conductance peaks in low temperature experiments on alkali metals and in gold. We then study the surface dynamic properties of different phases. Both surface phonons and surface self-diffusion of atoms are included in the linearized surface dynamics. It is found that inertial dynamics (phonons) always dominate the long-wavelength behavior at small time scales, including the critical points. (Abstract shortened by UMI.)

This thesis presents the techniques and results of our x-ray structural studies of strained Ga$ sb{1-x}$In$ sb{x}$As epilayers grown on GaAs (001) by metallorganic chemical vapor deposition. / By combining conventional x-ray techniques with newly developed glancing incidence and reflectivity measurements, we study both the out-of-plane and the in-plane structure. We also obtain direct information on the mechanisms of the structural relaxation which occurs in these systems. The techniques we have used are based on using a conventional x-ray source and could be widely used to characterize and study growth processes and sample quality. / Using the conventional characterization of the positions, widths, and intensities of Bragg peaks lattice parameters, domain sizes and strains have been evaluated. Studying the shape of the Bragg peak shows that the simple theoretical models based on the existence of a critical thickness due to dislocation can not be used to explain the structural relaxation observed. Our results based on thin (500 $ pm$ 12A, $x=0.19 pm 0.003$) and thick (40000 $ pm$ 1000A, $x=0.16 pm 0.01$) epilayers require a complicated microstructure in a transition region between the substrate and the surface of the epilayers.

The dynamics of a driven interface, with conservation of total volume under the interface, has been studied using a conserved Kardar-Parisi-Zhang-like equation. Dynamic renormalization group analyses have been performed on the nonlinear, far from equilibrium system in all practically interesting dimensions. The dynamic scaling form, which completely determines the fractal properties of the interface morphology, has been derived and found to be in extremely good agreement with numerical simulations. A new universality class of the growth regime, characterized by a novel superscaling relation, is obtained. For substrate dimension d = 1, the interface morphology is significantly less rough than that observed in the nonconserved system; at the critical dimension $d sb{c}$ = 2, the interface is found to be logarithmically rough. The dynamic roughening transition of the conserved driven interface has also been studied by taking into account a lattice pinning potential. This conserved system exhibits a true phase transition, rather than crossover behavior, as has been observed for nonconserved driven interfaces. The conserved nonlinear driving force is favorable for smoothing the interface, implying that the roughening transition shifts to higher temperatures as that driving force is increased. The nature of the phase transition remains the same as the equilibrium transition; the critical properties are controlled by a Kosterlitz-Thouless fixed point.

In the present thesis, we study the change in structural properties induced by ion beam irradiation of Ni/Fe and Co/Cu bilayers using various x-ray scattering techniques. These bilayers exhibit interesting GMR and magnetotransport properties. / We show that an N-step model is useful in simulating any given electron density profile. We test four different interface profile functions in fitting the reflectivity and conclude that the error-function profile best describes our samples. Different types of interfaces are introduced, namely graded and rough interfaces, together with a discussion of their representation and their effect on both specular reflectivity and non-specular x-ray intensity. / We develop a data acquisition and processing method in order to separate the specular and diffuse components of x-ray scattering and to obtain the normalized reflectivity. A computer program in C was developed to calculate the x-ray reflectivity (XRR) and diffuse scattering intensity and to fit the theoretical calculation to the experimental data using a non-linear least-squares fitting method. / By fitting the XRR data of six bilayers of Ni/Fe and Cu/Co of different thicknesses and deposition sequence, the electron density profiles are constructed for different irradiation doses, &phis;. The intermixing at interfaces is found to increase with increasing &phis;. No change in the bulk materials electron density is observed upon irradiation of four single layers of these materials. / A more detailed study is performed on Si/Ni(500A)/Fe(500A) bilayers. From diffuse-scan fits we find that as &phis; increases the interfaces become rougher, more jagged and the height-height correlation length of the roughness decreases. The intermixing can be approximated using the ballistic model of ion mixing. / Using high-angle x-ray diffraction (XRD) measurements, the samples are found to be polycrystalline with a strong texture of fcc Ni(111) and bcc Fe(101) parallel to the substrate surface. Both plane-view and cross-sectional transmission electron microscopy (TEM, XTEM) images show that in-plane and out-of-plane grain sizes increase with &phis;, in good agreement with out-of-plane grain sizes calculated from Bragg peaks. The high-angle x-ray Bragg peak positions agree well with selected-area electron diffraction (SAED) rings. The iron oxide parameters obtained from XTEM and SAED patterns agree well with XRR results.

We investigate the equilibrium properties and the relaxational dynamics of random heteropolymers in three dimensions. We proceed by studying an isolated random heteropolymer without an explicit solvent before studying different types of random heteropolymers in a monomeric solvent. Both equilibrium and relaxational data were obtained by performing extensive off-lattice molecular dynamics simulations. An equilibrium "phase diagram" is determined in all cases which facilitates the determination of a characteristic temperature separating extended states from collapsed states of the heteropolymer. This temperature is an increasing function of the strength of the random interactions and of the solvent density. It allows us to determine the appropriate initial and final temperatures to be used for the quenches from an extended coil to a collapsed globule. In particular for long isolated chains the heteropolymer collapse is a process which involves two distinct time regimes; both are energetically of stretched exponential form. Our simulation clearly shows the nature of the relaxation process where the formation of locally collapsed clusters takes place first followed by a global aggregation of the local blobs leading to the two collapse time regimes. Finally, we determine the effect of an explicit solvent on the collapse dynamics of a random heteropolymer. We bridge the difference between implicit and explicit solvents in two steps. First, we consider a heteropolymer with random interaction between the monomers, immersed in a purely repulsive solvent and we find that the rate of collapse increases with the strength of the random interaction but remains almost independent of the solvent density for higher values of the strength of the random interaction. Secondly, we look at a random heteropolymer with random interaction between the monomers and the solvent particles and we find that the rate of collapse increases slightly with density but is almost constant at low dens

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld instability, is of high technological importance. It can be associated with the dislocation-free island-on-layer growth mode in epitaxy which is an essential process used in the semiconductor industry. / In our model, the elastic field is coupled to a scalar order parameter in such a way that the solid supports shear whereas the liquid phase does not. Thus, the order parameter has a transparent meaning in the context of liquid-solid phase transitions. / We show that our model reduces in the appropriate limits to the sharp-interface equation, which is the traditional formulation of the problem. Inherent in our description is the proper treatment of non-linearities which avoids the numerical deficiencies of previous approaches and allows numerical studies in two and three dimensions. / To test our model, we perform a numerical linear stability analysis and obtain a dispersion relation which agrees with analytical results. We study the non-linear regime by measuring the Fourier transform of the height-height correlation function. We observe that, as strain is relieved, interfacial structures, corresponding to different wave numbers, coarsen. Furthermore, we find that the structure factor shows scale invariance. We expect that our result on transient coarsening phenomena can be measured through microscopy or x-ray diffraction.

At low temperature, we have used thermal conductivity as a directional probe of the residual normal fluid in two superconductors, UPd2Al 3 (a heavy fermion) and YBa2Cu3O7-delta (a high-Tc cuprate). By extrapolating our measurements to zero temperature, we can shed light on zero energy quasiparticles and the structure of the superconducting gap. / For both superconductors, we review measurements pertaining to the density of states. In the case of the heavy fermion superconductor UPd2Al 3, we have found a finite anisotropy between b axis and c axis heat conduction, which excludes those gap structures with only zeroes along c or in the equatorial plane of a spherical Fermi surface; however, our results are consistent for two line nodes equidistant from the equatorial plane, as in the A 1g gap. Comparisons to theory developed for UPt3 show qualitative agreement with two hybrid gaps with strong spin-orbit coupling, of E2u and E 1g symmetry. / For YBa2Cu3O7-delta, because the gap symmetry has been established as dx2-y2 , we can go much further as regards a quantitative analysis. The anisotropy in the thermal conductivity was measured along both high symmetry directions. A residual T-linear term in kappa(T) was observed in both directions. In the CuO2 planes (J∥ a) the magnitude of the residual normal fluid conduction is perfectly consistent with the temperature dependence of the penetration depth, within the theory for a d-wave superconductor. The value for J∥b is slightly larger, yielding an anisotropy ratio of 1.3 +/- 0.3. This is considerably weaker than that observed in the normal state resistivity, pointing to a suppressed heat conduction by quasiparticles in the chains, either due to strong defect scattering or a gapped excitation spectrum. / With the application of an external magnetic field (up to 8 T), we can study the effect of vortices on quasiparticle transport. The residual linear term increases with field, directly reflecting the occupation of extended quasiparticle states. A study for different Zn impurity concentrations reveals a good agreement with recent calculations for a d-wave gap. The magnitude of the suppression indicates that Zn impurity scattering needs to be treated in the resonant impurity scattering limit, until now an unverified assumption. Together with specific heat measurements, we obtain a quantitative measure of the gap near the nodes.

The metallic adhesion and tunneling properties of an atomically defined junction were measured and analyzed. The junction consisted of a tip opposing a flat surface in the scanning probe microscopy (SPM) configuration. Measurements were performed in ultrahigh vacuum (UHV) at 150 K. Sub-nN force resolution was achieved on a stiff cantilever beam employing an in-situ differential interferometer. Tips were prepared from W and Ir wire and imaged with atomic resolution in-situ using field ion microscopy (FIM). Ultrasharp tips with an apex radius of 20--30 A were fabricated from single crystal W(111) wire and engineered with FIM to terminate in only three atoms. Calculations indicate that for those tips metallic adhesion forces dominate over van der Waals and capacitive electrostatic forces. The sample was a thin (111) oriented Au film. Metallic adhesion forces and the tunneling current were measured simultaneously for the W-Au system as a function of tip sample separation. In contrast to theoretical simulations the system featured exceptional mechanical stability with adhesive forces of up to 5 nN. In particular no indications of a sudden jump-to-contact, which is commonly believed to be an inherent property of metallic contacts, were found. Furthermore, the range over which the metallic adhesion forces act is four times larger than expected. Experiments with sharp but not atomically defined W tips corroborate those results. The observed long interaction range is discussed in the framework of various models. Some of the consequences of this new property for force microscopy applications are pointed out.

An extensive study of a-FexTM 1-xZr2 with TM = {V, Cr, Mn, Co, Ni, Cu} was undertaken in order to gain insight into the glassy structure, the metastable "big-cube" structure of the intermediate crystallisation product, and the evolution process involved therein. The stability of the glassy state was examined by differential scanning calorimetry (DSC). Generally higher temperatures and more negative enthalpies of crystallisation were observed for the glass system where Fe was substituted with {Co, Ni, Cu} than for the system where Fe was substituted with {V, Cr, Mn}. A proposed hypothetical crystallisation mechanism involved in the evolution of the metastable cF96 state (instead of the equilibrium tI12 state) was tested. Oxygen impurities present in the amorphous state were shown to be responsible for nucleating the cF96 big cube. Upon removal of the oxygen nucleation sites through hydrogenation of the glasses, the crystallisation proceeded directly to the equilibrium tetragonal structure bypassing the metastable phase. The validity of an assumed invariant structure in late transition-early transition metal (LT-ET) binary glasses was examined by means of Mossbauer spectroscopy. Variations in isomer shift (delta) and quadrupole splitting (Delta) upon TM substitution were consistent with variations in the density of states (DOS) at the Fermi level (EF). An assumed constant structure for (4d ET)-(3d LT) glasses is indeed justified. Variations in atomic packing were followed by measuring Delta. Delta increased as the atomic number of the TM increased. For the a-Fe xCu1-xZr 2 series, a break in the concentration dependence of Delta at x ≈ 0.3 is observed which mirrors the change in crystallisation from cF96 to tI6. Furthermore, comparisons of the glassy, metastable cubic and equilibrium tetragonal Mossbauer spectral data show obvious similarities between the glass and big cube which strongly suggest the existence of a common local (short-range) order between the two