We study the kinetics of domain growth in deeply quenched anisotropic ferromagnets in the presence of a small external field H, using three simulation methods in two dimensions. In particular, we concentrate on the time evolution of the inverse perimeter density, squared magnetization, and structure factor, all of which characterize the domain morphology. The inverse perimeter density evolves as $R sp2$(t,H) $ sim$ t$ sp{n}$, where n = 1 for early time and n = 2 for late time. We characterize the crossover behavior of this growth law and demonstrate that the inverse perimeter density behaves like $R sp2$(t,H) = $ alpha$(H)tf($tH sp2$) where f(x) $ to$ 1 as x $ to$ 0 and f(x) $ to$ x as x $ to$ $ infty$. We further demonstrate that the squared magnetization and the structure factor do not scale, indicating that not all lengths in the problem behave in the fashion mentioned above. An analytical formulation of the problem is also studied with a perturbation theory in the limit H $ to$ 0. The first term is calculated and agrees qualitatively with the computer simulations.

The mixed state of type II superconductors is an ideal medium for the study of correlated systems since the density of vortices which penetrate the sample, as well as the driving force, can be tuned such as to measure their effects on correlations. The weak pinning character of the Fe xNi1-xZr2 metal glasses permits vortex phases to be probed by dissipative transport (longitudinal and Hall) measurements. The complete phase diagram in this regime is mapped out as a function of magnetic field, driving current and temperature using results from longitudinal resistance measurements. The longitudinal measurements show a huge peak effect with a driving force induced pinning phase known to arise from a disordering transition. The Hall resistance measurements lead to remarkable new results: a critical angle dependence of the vortex flow direction when entering or leaving the disordered phase is revealed, which suggests the existence of orientational phase transitions.

Although the study of thermal transport in condensed matter has a very long history, it continues to be an active field of work due to its importance in many applications. The research subject reported in this thesis is on theoretical investigations of thermal energy transport in systems whose linear dimension is less than the wavelength of thermal phonons. Such situations occur in mesoscopic and nanoscopic scale dielectric structures which can now be fabricated in a number of laboratories. Due to the small system dimensions, phonons must be treated as waves. Thermal energy transport, therefore, must be treated as phonon wave propagation through the system. / After reviewing the general physics of thermal energy transport in the classical regime, we derive, for dielectric materials, a formula for thermal energy flux in devices involving multi-terminals each connected to a thermal reservoir at local equilibrium. The energy flux is driven by a temperature bias and traverses the system by virtue of phonon wave scattering. A multi-terminal thermal conductance formula is derived in terms of phonon transmission coefficient. Using our theoretical formulation, we investigate thermal transport properties of both two-terminal and four-terminal dielectric devices by solving the quantum scattering problem using a mode matching numerical technique. / For thermal transport in a T-shaped dielectric nanostructure with two-terminals at low temperature, due to quantum interference the transmission coefficient of phonons becomes quite complicated. We found that the value of phonon transmission coefficients at zero energy may be unity or zero depending on a geometrical ratio of the nanostructure. The transmission has an oscillation behavior with quasi-periodicity and irregularity. The thermal conductance is found to increase monotonically with temperature---a result that we conclude to be generally true for any two-terminal device. We confirm the existence of the universal quantum of thermal conductance which exists at the low temperature limit, and such a quantum is robust against all the system parameters. / The physical behavior of four-terminal thermal conductance for mesoscopic dielectric systems with arbitrary shapes of scattering region is also investigated in detail. If we make a two-terminal measurement in the four-terminal device, the two-terminal conductance is a monotonically increasing function of temperature, and is equal to the universal quantum of thermal conductance masked by a geometric factor. If we make a four-terminal measurement, the four-terminal conductance has a non-monotonic dependence. In the low temperature limit, we predict that the four-terminal conductance diverges inversely proportional to temperature. / Finally, we discuss an interesting theoretical problem on the general behavior of thermal conductance for multi-terminal systems when thermal carriers satisfy fractional exclusion statistics. Our analysis allows us to conclude that results for fractional exclusion statistics are quite different from those of the Bose-Einstein statistics.

The discovery of fullerenes and carbon nanotubes has been very significant to the field of nanotechnology by providing an abundance of stable, highly symmetric, non-reactive, and relatively large molecules that can, in principle, be manipulated one at a time. At the present stage, a theoretical effort should be carried out in order to find and understand novel phenomena in molecule-based nanostructures which could serve as a basis for fabricating useful molecular devices. In this thesis we investigate from first-principles the transport properties of molecular devices: fullerene and carbon nanotube systems. / We begin with charge transport in carbon nanotubes with oxygen, and find that the interaction between oxygen molecules and carbon nanotubes significantly modifies the electronic structure near the Fermi level for both zigzag and armchair tubes. The subtle difference of the adsorption sites of oxygen and the distance between oxygen and nanotubes can cause totally different results of their transport properties. / Then we investigate current flow from the point of view of current density distribution in molecular devices, for current density gives local information of nonequilibrium transport, thereby providing useful and vivid insight to transport properties of molecular electronics. It has been found when an intrinsic carbon nanotube is doped with either a boron or a nitrogen atoms through a replacement of a carbon atom, the local physical properties around the impurity atoms (boron or nitrogen) undergo a significant change, resulting in a dramatic change of the local current distribution. It is suggested that there appears a chiral current flow in the B- and N-doped armchair nanotubes near the impurity. As for a gated C 60 molecular device, the current distribution and the total current flow are both obviously affected by the gate voltage, which indicates the importance of the gate voltage in such a molecular device. / Finally, we discuss the contact effects on transport properties of the molecular devices. We study the effects of the contact geometry as well as the electrode material and find that different orientations of C 60 connected to Au(111) leads can cause significant changes in the current-voltage (I-V) characteristics of such C60 molecular devices. On the other hand, the electrode material is crucial to obtain low resistance ohmic contacts. Our first-principles calculations of transport suggest that Ti has higher affinity for carbide formation. So the choice of proper electrode materials will play an important role in the design of nanoscale devices.

A combined ultra-high vacuum scanning tunneling microscope, atomic force microscope, and field ion microscope UHV (STM/AFM/FIM) system was used to study mechanical and electronic interactions at the atomic scale. A surface science system, consisting of an Auger electron spectrometer, UHV evaporators, ion sputter gun and annealing capabilities, was designed and constructed. A new force sensor preparation method was developed suitable for high stability imaging. Using this improved system, we studied W tip- Au(111) sample interactions in the regimes from weak coupling to strong interaction and simultaneously measured current changes from pA to muA. Close correlation between conductance and interaction forces in a STM configuration was observed. In particular, the electrical and mechanical points of contact were determined based on the simultaneously observed mechanical and electrical response. These points of contact as defined by force and current measurements coincide within measurement error. Ab initio calculations of the current and force as a function of distance in the tunneling regime are in quantitative agreement with experimental results. Simultaneous force-distance and current-distance curves are proven to be essential in understanding processes occurring in scanning tunneling and force microscopies. Finally, the observed contact phenomena and energy dissipation are discussed in the context of nanoelectronics and noncontact atomic force microscopy.

We study theoretically a mechanical oscillator coupled to a superconducting single-electron transistor (SSET), focussing on the regime where incoherent Cooper pair tunnelling in the SSET leads to a negative damping instability of the oscillator. In this regime, large oscillator motion modulates tunnelling in the SSET, which in turn affects the oscillator. This interplay leads to interesting strong feedback effects, including a highly non-thermal stationary oscillator state and a significant enhancement of the low-frequency current noise in the SSET. These effects and others are reminiscent of laser physics: the SSET corresponds to population-inverted atoms while the oscillator corresponds to cavity electro-magnetic field modes. We discuss the extent of this analogy and investigate the linewidth of the oscillator's noise spectrum. Our results are relevant to current experiments, and we point out several feasible measurements that could be done to observe strong feedback effects.

In an attempt to understand how surface contacts affect friction, and to bridge the gap between single contact and large scale friction studies, silicon and PDMS multi-tip arrays were produced in the McGill Microfabrication Facility. An apparatus was constructed to rub the tip arrays on a glass surface while creating a diffraction pattern using scattered laser light. Changes in tip ordering could be correlated to changes in the diffraction pattern. Values for tip-to-tip separation were extracted from the diffraction pattern and it was found that the PDMS tip array compressed by 10% after sliding. / Simulations of an AFM tip rubbing along an ionic surface were also performed. Experimentally observed stick-slip behavior was reproduced in the simulation, and simulated contact stiffness values corresponded to experimental results. By varying the flexibility of the tip and the surface it was determined that tip compliance is the dominant factor that controls stick-slip behavior.

Avalanche Photodiode (APD) is a compact and rugged device, with single photon detection capability and high quantum efficiency. It is a good candidate as a detector to observe irradiation damage to silicon devices and the irradiation induced defects. In this thesis, we have observed the bistable defects and the multistable defects in the APD. We can also observe the time evolution of defect formation and annihilation with time resolution of 10 ms. Also we develop a technique to observe the evolution of defects in real time with an improved time resolution of 1 $ mu s$.

The thermal conductivity $ kappa$ of the high-temperature superconductor $ rm YBa sb2Cu sb3O sb{7- delta}$ has been the subject of numerous investigations in recent years. Previous measurements show that $ kappa$: (1) exhibits a large peak in the superconducting state; (2) is anisotropic in the basal plane of the orthorhombic crystal structure. The main two subjects of this thesis are: (1) the origin of the peak and (2) a detailed investigation of the anisotropy. / In order to investigate the relative contribution of electrons and phonons to the heat conduction in YBCO, we have measured the thermal and electrical conductivities of high-quality twinned and detwinned crystals, with different levels of Zn-doping (from 0% to 3%). We found that the peak was rapidly suppressed by the impurities. Two scenarios are used to explain our results, attributing the effect to decrease in the carrier mean free path of either the electrons or the phonons. / As for the anisotropy between the a-axis and the b-axis, only two previous studies had previously been done. We find some new striking features: (1) a peak appears in $ kappa sb{chain}$ below 50 K, revealed as a result of our using of higher purity samples. (2) this peak is similar to that of $ kappa sb{a}$ below $T sb{c} (i.e., kappa sb{plane}),$ which we take as the evidence for the growth of superfluid density in the chains below 60 K. We discuss these results in terms of a model of single-electron tunneling between chains and planes.

We examine tracer diffusion in lipid bilayer membranes containing either cholesterol or lanosterol, using a random lattice Ising model. Specifically the model is a two-state off lattice tethered network of hard disks which is dynamically triangulated and the interactions between the hard disks are only effective along the tethers linking the disks. The model was already applied to lipid-sterol systems and was successful in reproducing the phase diagrams and related physical properties. In this thesis we apply this model in conjunction with Monte Carlo simulation methods as follows. We calculate the diffusion constant for lipid-cholesterol and lipid-lanosterol bilayer membranes both as function of temperature and sterol concentration in all accessible regions of the relevant phase diagrams. Comparison with experiment and comments on sterol related evolution are included.