In this thesis, non-equilibrium Green's function techniques in combination with the time-dependent non-crossing aprroximation are utilized to calculate the transient currents through a quantum dot in the Kondo regime subject to sudden perturbations. We first present novel numerical algorithms which enable relatively fast calculations. We then employ these algorithms to study the transient current through a quantum dot which is symmetrically coupled to metallic leads and its coupling to the leads is abruptly switched such that the Kondo effect is present in the final state. The timescales for the approach to equilibrium are shown to be the same as the ones when the energy level of the dot is suddenly switched. Finally, we study the transient currents in a quantum dot asymmetrically coupled to metallic leads resulting from the abrupt change of the dot level. We show that for asymmetric coupling, sharp features in the density of states of the leads can induce oscillations in the current through the dot. The amplitude of these oscillations increases as the temperature is reduced and saturates below the Kondo temperature. We discuss the microscopic origin of these oscillations and comment on the possibility for their experimental detection.

In this thesis, the plasmon hybridization method is extended theoretically to explore the optical properties of curvilinear particles, high symmetry clusters, and infinite periodic systems of nanoparticles. Plasmon hybridization is a recently-developed theory used to describe the collective oscillations of conduction electrons in metallic nanoparticles (plasmons). Here curvilinear particles refer to solid nanoparticles, dielectric cavities in an infinite metal, or nanoparticles consisting of a dielectric core surrounded by a thin metallic shell (core/shell particles) that can be described using a coordinate system with a completely separable solution to the Laplace equation. I find that there is a common form for the plasmon frequencies of such particles among all completely separable coordinate systems and that the plasmons of core/shell particles can be viewed as a hybridization resulting from the interaction of solid particle and cavity plasmons. I specifically analyze the plasmons of prolate, oblate, and cylindrical particles, three experimentally relevant geometries. High symmetry clusters are collections of nanoparticles that exhibit the symmetry of a point group. I study the plasmons of nanosphere trimers (equilateral triangles, group D3 h), quadrumers (squares, group D4 h), and tetramers (tetrahedra, group Td). This study shows that the plasmons of these systems are composed of linear combinations of plasmons from each individual particle and may be classified into the irreducible representations corresponding to the point group to which each system belongs. This represents a step forward in understanding the underlying concepts behind the plasmon modes of multi-particle systems. The periodic systems that are examined in this thesis include a one-dimensional infinite nanosphere chain and two-dimensional hexagonal and square nanosphere arrays. The calculated plasmon energies are shown to agree very well with Finite Difference Time Domain calculations, a somewhat surprising result considering the quasistatic nature of plasmon hybridization. In contrast to other modeling methods, wherein a nanosystem's plasmon frequencies are calculated computationally or as the poles of a polarizability function, plasmon hybridization provides a physical picture of the plasmon modes in each system in analogy with molecular orbital theory and thus proves to be an essential tool in understanding the fundamental science behind the plasmonics of these systems.

Metal nanoshells possess plasmon resonances that are controlled by the geometry of the nanoparticle. Because nanoshell plasmon resonances can be readily predicted by the plasmon hybridization model or Mie scattering theory, it is possible to design a nanoshell to possess specifically chosen plasmonic properties. This thesis examines how to optimize the nanoshell geometry for various sensing applications. Although the nanoshell plasmon can be described within the quasistatic limit using plasmon hybridization, experimentally feasible nanoshell plasmons are also influenced by finite size effects. It is thus important to gain insight into the properties of the nanoshell plasmon in this mesoscopic regime in order to optimize the nanoshell geometry for applications such as the plasmon enhanced fluorescence. We examine the roles of the nanoparticle plasmon resonance energy and nanoparticle scattering cross-section on the fluorescent emission of indocyanine green (ICG). We find that enhancement of the molecular fluorescence is optimized when the nanoshell exhibits a large scattering cross section and a plasmon resonance energy which corresponds to the emission frequency of ICG. Another potential biomedical application for nanoshell is their use as surface plasmon resonance (SPR) sensors. We investigate the geometrical parameters that determine the sensitivity of an Au-nanoshell SPR sensor. It was found that the sensitivity of the nanoshell plasmon to its embedding medium depends primarily on total nanoshell size and less sensitively on core/shell ratio. It is clear from these studies that the efficacy of a nanoshell used in a particular application depends on more parameters than just the plasmon resonance energy.

Magnetic flux threading a single-walled carbon nanotube (SWNT) is predicted to influence its electronic structure through the Aharonov-Bohm (AB) effect, causing bandgap oscillations and absorption peaks splitting. In order to verify these predictions, near infrared (NIR) photoluminescence (PL) and visible-NIR absorption in the Voigt geometry were measured at room temperature in external magnetic field (B) up to 74 T. The used aqueous surfactant solubilized SWNT samples show excitonic interband absorption peaks coming from a range of nanotube chiralities present in the sample. At fields B > 30 T, PL peaks showed red shifts and changes in peak widths. Magneto-PL spectra were successfully simulated, demonstrating that the observed spectral changes can be understood in terms of magnetic alignment of SWNTs (due to their predicted anisotropy magnetic properties) and B dependent changes of the bandgap due to the AB effect. By using the measured B-induced nanotube alignment and the measured average length of nanotubes in the sample, we estimated SWNT magnetic anisotropy to be 1.4 x 10-5 emu/mol, consistent with theoretical predictions. At B > 55 T, clear absorption peak splittings were observed, with splitting rates of 1 meV/T in good agreement with theoretical predictions. Recent theory predicts a dark singlet exciton state (below the only bright singlet state) which brightens as B is applied. Our observation of two bright excitons at high B demonstrates that magnetic field is indeed capable of brightening dark excitons.

Mott polarimeters are used in many areas of physics to determine the spin polarization of electrons in studies of processes dependent on the electron's intrinsic spin angular momentum and associated spin magnetic moment. Mott polarimeters work by measuring the left-right asymmetry in the spatial distribution of electrons scattered from high-Z nuclei. The polarization of the incident electrons is related to the measured asymmetry via a parameter known as the effective asymmetry (Sherman) function, S$\sb{\rm eff}$, which must be determined through calibration. This work describes a novel technique for calibrating a Mott polarimeter that makes use of electrons of accurately known polarization obtained through Penning ionization reactions involving electron spin polarized He(2$\sp3$S) metastable atoms. This technique has been used to calibrate a compact retarding-potential Mott polarimeter, and the values of S$\sb{\rm eff}$ are presented for both gold and thorium target foils under a variety of operating conditions.

We present calculations of the lifetime broadening and the shifts of hydrogen atomic levels (both ground and excited levels) near impurity covered jellium metal surfaces using complex scaling technique. The impurities which are used in the calculations are Na, Cl and Cs. It has long been known, that the presence of the impurities on metal surfaces can both shift position and change the widths of the electronic levels. It is shown that for an accurate description of the system it is important to use support basis functions centered on the impurity. We also investigate the accuracy of a classical treatment of electron transfer in atom metal collisions and compare it to Monte Carlo based quantum mechanical calculations. It is shown that for slow particles the treatments deviate from each other, thus giving different predictions for the sticking effects on the surface.

UHV-compatible Mott polarimeters that employ electron accelerating voltages of $\sim$20kV have been designed and tested. The efficiency of the polarimeters, $\sim$3 $\times$ 10$\sp{-5}$, is competitive with those provided by other polarimeters, but the present polarimeters are considerably simpler and more compact. The scattering efficiency of the polarimeters is 2.2 $\times$ 10$\sp{-3}$, which makes it possible to accurately measure electron spin polarizations using input beam currents as low as 10$\sp{-14}$A. One polarimeter design incorporates an in-line retarding potential energy analyzer with an energy resolution $\sim$0.5eV, and is suitable for a wide variety of applications requiring energy- and angle-resolved polarization measurements.

Positively charged clusters of V, Nb, Ta, Co, Rh, Ir, and Ni in the size range of 3-26 atoms were generated by laser vaporization in a supersonic nozzle and injected into the ion trap of a Fourier transform ion cyclotron resonance apparatus, where they were studied by exposing them to hydrogen gas. Some clusters experience structural changes during the chemisorption process, and some clusters have multiple stable isomers. The reactivity of positive V, Nb, and Ta clusters toward H$\sb2$ increases with cluster size, but the reactivity oscillates so that the even clusters can be several orders of magnitude less reactive than their odd neighbors. The reactivity of positive Co, Rh, Ir, and Ni clusters toward H$\sb2$ varies with the cluster size, but the variation is smooth. In general clusters made of atoms with the same number of valence electrons behave quite similarly. The high reactivity of most positive clusters is attributed to unoccupied d-like states lying near the fermi level--these states are needed to avoid the Pauli repulsion, which creates the activation barrier for the H$\sb2$ chemisorption.

This thesis studies superradiance and subradiance in the normal modes of excitation of systems of resonant nuclei. The nuclei are treated as classical electric dipole oscillators interacting through their radiation fields. This coupling radically alters the radiative decay of the system relative to the decay of an isolated nucleus, and leads to both superradiant and subradiant states with strongly enhanced or suppressed radiative decay rates, and with normal mode frequencies which can be strongly shifted from the natural resonance frequency. This issue is of considerable current interest because it is now possible to create spatially coherent single exciton nuclear states by illuminating crystals containing resonant Mossbauer nuclei with synchrotron radiation pulses. The purpose of this thesis is to solve for the radiative eigenmodes in a system of nuclei and to investigate superradiance and subradiance both in the eigenmode solutions and in the synchrotron radiation produced nuclear exciton state.

Previous experiments have shown that Metastable De-excitation Spectroscopy (MDS) provides a valuable probe of surface electronic and magnetic structure. Spin labelling of the excited electron can yield additional information about the de-excitation mechanisms. In such experiments, neon ($\sp3$P$\sb2$) and argon ($\sp3$P$\sb2$) metastable atoms are spin-labelled (polarized) by laser optical pumping, and their polarization measured by a Stern-Gerlach analyzer. In the present work, a Time-of-Flight (TOF) velocity selection capability has been implemented in an existing MDS apparatus to permit accurate determination of the metastable atom polarization achieved by optical pumping. The data show that polarizations in excess of 85% and 92% may be obtained for Ne ($\sp3$P$\sb2$) and Ar ($\sp3$P$\sb2$), respectively. TOF techniques are also used to investigate the velocity distribution of metastable atoms in the beam, and to eliminate spurious signals due to photon-surface interactions.