Ultracold atoms have emerged as an indispensable setting to study quantum many-body systems. Recent experimental and theoretical work has explored the curious phases and novel properties of Bose-Einstein Condensate with optical lattices, and Bose-Einstein Condensate with light-induced artificial spin-orbit coupling. In this thesis, we report our research on these two types of boson systems. In the first topic, in contrast with calculations of bosons in optical lattices that focus on the tight-binding regime, we note that the single-particle states of bosons in a periodic potential generally satisfy the Mathieu equation, and have developed a formalism for studying bosons in an optical lattice using the Mathieu equation. Moreover, based on this formalism, we have proposed a self-consistent scheme for describing interacting bosons in an optical lattice using Hartree Fock approximation. We apply this scheme to quantify the effects of inter-atomic interactions on the properties of bosons in an optical lattice, as exhibited in the comparison between observables of non-interacting and interacting systems, such as the superfluid transition temperature and momentum distribution as probed in time-of-flight expansion. In the second topic, the phases of a Bose-Einstein condensate with light-induced spin-orbit coupling are studied within the mean-field approximation. We obtain the phase diagram at fixed chemical potential and at fixed density for bosons with spin-orbit coupling, finding a regime of phase separation and a regime in which the bosons condensed into a mixed phase. We determine how this phase diagram evolves as a function of the atom interaction parameters and as a function of the strength of light-atom coupling. The mixed phase is found to be stable for sufficiently small light-atom coupling. Specifically, we show that the structure of the phase diagram at fixed chemical potential suggests an unusual density dependence for the mixed phase in a harmonic trapping potential, in which the density of one spin increases with increasing radius, suggesting a unique experimental signature of this state. The collective Bogoliubov sound mode is shown to also provide a signature of the mixed phase, vanishing as the boundary to the regime of phase separation is approached. Together, in these two topics we address the need to enhance the understanding of the unconventional physical properties of Bose-Einstein Condensate in a controlled electromagnetic environment (optical lattices, Raman lasers, etc.), and provide predictions for possible experimental findings.

A model heterogeneous catalyst inspired by a real catalyst is synthesized for the purpose of understanding how it works. To make such model catalysts, we choose to evaporate metal atoms on metal oxide single crystals and measure them under UHV conditions. The study of model catalysts could advance the understandings of fundamental catalytic properties of real catalysts and helps to optimize or redesign industrial catalysts. In our experiments, many ultra-high vacuum (UHV) techniques have been employed to investigate the atomic and electronic structure of the surface as well as the interface of the prepared samples. In particular, the surface-sensitive tools such as electron energy loss spectra (EELS) and low energy ion scattering (LEIS) spectra provide us detailed information of the surface modification. In this dissertation, we confine our attention to three popular catalysts: Cu on ZnO, Au on ZnO and Cu on TiO2, which play primary roles on modern methanol industry. For instance, Au on ZnO and Cu on ZnO are important catalysts for methanol synthesis, water-shift reaction and methanol-steam reforming, while Cu on TiO2 possesses a high photocatalytic activity for photoreduction of CO2 into methanol. It becomes important for us to develop an understanding of which factors determine the functions of the prepared samples. Different metal growth models are observed for the above samples, due to the varied metal-oxide interactions. At the high substrate temperature, full encapsulation of metal nanoparticles takes place to all of the above samples, which dramatically changes the adsorption behavior and catalytic performance. It provides a strong indication that these thin encapsulation layers are very different from their bulk materials in both geometric and electronic sides. The charge transfer in the interface may be responsible for the modification of geometric and electronic structure of surface, and results in high-thermal stability of these ultra-thin films. The above reconstruction leads to an exceptional catalytic activity of CO oxidation through a different reaction kinetics and mechanism. The CO oxidation experiments show a direct relation between encapsulation rate and reaction rate, which indicates the active sites should be localized at these thin oxide films rather than the metal nanoparticles.

Reactions involving radioactive nuclei play an important role in stellar explosions, but limited experimental information is available due to difficulties in producing and studying radioactive nuclei. Several facilities aim to provide greater access to these unstable isotopes at higher intensities, but more efficient and selective techniques and devices are required to be able to study many important reactions. The Array for Nuclear Astrophysics and Structure with Exotic Nuclei (ANASEN), a charged particle detector designed by Louisiana State University (LSU) and Florida State University (FSU), was created for this purpose. ANASEN is used to study the reactions important for the αp- and rp- processes with proton-rich exotic nuclei by providing essentially complete solid angle coverage through an array of 40 silicon-strip detectors backed with CsI(Tl) scintillators, covering an area of roughly 1300 cm2. ANASEN includes an active gas target/detector using a position-sensitive annular gas proportional counter that allows direct measurement of (α,p) reactions in inverse kinematics. Measurements with a partial implementation of ANASEN were first performed at the RESonator SOLenoid Upscale Transmission (RESOLUT) radioactive beam facility of FSU during the summer of 2011. This included stable beam experiments and measurements of the 17F(p,p)17F and 17F(p,α)14O reactions that are important for understanding the structure of 18Ne and the 14O(α,p)17F reaction rate. We report in detail on one experiment using a 55 MeV beam of 17F to bombard a 2 mg/cm2 thick polypropylene target. Scattered protons were detected in a silicon strip detector array in coincidence with recoiling heavy ions in a gas ionization chamber that provided clean identification of the reaction channels. The center-of-mass energy for each event was reconstructed from the proton energy and angle, allowing the 17F(p,p)17F elastic scattering cross section to be measured between center-of-mass energies of 1.95 MeV and 3.06 MeV. The measured cross sections were fit with theoretical cross sections using phenomenological R-matrix theory. We conclusively observe two resonances. One corresponds to a 1- state in 18Ne, and we determine Ex = 6142 (5)stat (8)sys keV with total width Γ = 45 (12) keV. We are also able to set a lower limit on the proton partial width to the ground state of Γp > 15 keV at the 90% confidence level. We also observe a 2- state that we determine to be at Ex = 6373 (8)stat (8)sys keV with a total width equal to the partial width to the ground state of Γ = Γp = of 87 (15) keV. While we can not resolve a previously reported 3- resonance in this same energy regime, we can set a stringent limit on its proton partial width to the 17F ground state of Γp < 4 keV at the 90% confidence level.

Neutrinos are a useful tool that serves as an immediate probe of the Suns core providing insight into the details of the Suns energy production, internal composition and structure. Across the globe a number of solar neutrinos experiments have helped to clarify various characteristics of the solar neutrino spectrum. However, little experimental information is known regarding low-energy solar neutrinos, which comprise about 90% of the total solar neutrino spectrum. With this in mind, we are developing the Low Energy Solar Neutrino Spectrometer (LENS), an indium-based liquid scintillator detector with the capability to precisely measure the full spectrum of solar neutrinos, including pp, 7Be, pep, and CNO neutrinos, through the charged current reaction. Due to the high sensitivity required to detect low energy neutrinos, the LENS concept must aim for precise time and spatial correlations. This is to be accomplished using a highly segmented optical lattice architecture, where total internal reflection of light produces excellent spatial resolution. A program of R&D is being conducted to test the future performance of the LENS detector technology. This thesis focuses on construction and testing of the first prototype, μLENS, a small-scale detector prototype with 110 liters of Linear alkylbenzene (LAB) scintillator designed to test construction techniques and light transport in the scintillation lattice architecture. A number of measurements with the μLENS prototype were performed. We studied light channeling inside the detector by illuminating it with external radioactive sources. The patterns of light reaching the outer surface of the μLENS were measured with an array of photomultipliers. A data acquisition system and analysis codes were developed to collect and process the data. The γ background rates inside the Kimballton Underground Research Facility (KURF) were also studied using a NaI detector and the μLENS prototype. We also performed a test of light transport with external LEDs. The next step in the development of LENS is construction of miniLENS, a next generation prototype detector that will include external shielding to probe the absolute sensitivity of the LENS concept at neutrino rates.

The main technical problem with background independent approaches to quantum gravity is inapplicability of standard quantum field theory methods. New methods are needed which would be adapted to the basic principles of General Relativity. Topological field theory is a model which provides natural tools for background independent quantum gravity. It is exactly soluble and, at the same time, diffeomorphism invariant. Applications of topological field theory to quantum gravity include description of boundary states of quantum General Relativity, formulation of quantum gravity as a constrained topological field theory, and a new perturbation theory which uses topological field theory as a starting point. The later is the central theme of the thesis. Unlike the traditional perturbation theory it does not require splitting metric into a background and fluctuations, it is exactly diffeomorphism invariant order by order, and the coupling constant of this theory is dimensionless. We describe the basic ideas and techniques of this perturbation theory as well as inclusion of matter particles, boundary states, and other necessary tools for studying scattering problem in background independent quantum gravity.

Better understanding of protein folding process can provide physical insights on the function of proteins and makes it possible to benefit from genetic information accumulated so far. Protein folding process normally takes place in less than seconds but even seconds are beyond reach of current computational power for simulations on a system of all-atom detail. Hence, to model and explore protein folding process it is crucial to construct a proper model that can adequately describe the physical process and mechanism for the relevant time scale. We discuss the reduced off-lattice model that can express <em>&alpha;</em>-helix and <em>&beta;</em>-hairpin conformations defined solely by a given sequence in order to investigate a protein folding mechanism of conformations such as a <em>&beta;</em>-hairpin and also to investigate conformational conversions in proteins. The first two chapters introduce and review essential concepts in protein folding modelling physical interaction in proteins, various simple models, and also review computational methods, in particular, the Metropolis Monte Carlo method, its dynamic interpretation and thermodynamic Monte Carlo algorithms. Chapter 3 describes the minimalist model that represents both <em>&alpha;</em>-helix and <em>&beta;</em>-sheet conformations using simple potentials. The native conformation can be specified by the sequence without particular conformational biases to a reference state. In Chapter 4, the model is used to investigate the folding mechanism of <em>&beta;</em>-hairpins exhaustively using the dynamic Monte Carlo and a thermodynamic Monte Carlo method an effcient combination of the multicanonical Monte Carlo and the weighted histogram analysis method. We show that the major folding pathways and folding rate depend on the location of a hydrophobic. The conformational conversions between <em>&alpha;</em>-helix and <em>&beta;</em>-sheet conformations are examined in Chapter 5 and 6. First, the conformational conversion due to mutation in a non-hydrophobic system and then the conformational conversion due to mutation with a hydrophobic pair at a different position at various temperatures are examined.

In this thesis we study the interactions of ions and cationic peptides with a negatively charged lipid bilayer in an ionic solution where the electrostatic interactions are screened. <br /><br /> We first examine the problem of charge renormalization and inversion of a highly charged bilayer with low dielectric constant. To be specific, we consider an asymmetrically charged lipid bilayer, in which only one layer is negatively charged. In particular, we study how dielectric discontinuities and charge correlations among lipid charges and condensed counterions influence the effective charge of the surface. When counterions are monovalent, e. g. , Na⁺, our mean-field approach implies that dielectric discontinuities can enhance counterion condensation. A simple scaling picture shows how the effects of dielectric discontinuities and surface-charge distributions are intertwined: Dielectric discontinuities diminish condensation if the backbone charge is uniformly smeared out while counterions are localized in space; they can, however, enhance condensation when the backbone charge is discrete. In the presence of asymmetric salts such as CaCl₂, we find that the correlation effect, treated at the Gaussian level, is more pronounced when the surface has a lower dielectric constant, inverting the sign of the charge at a smaller value of Ca²⁺ concentration. <br /><br /> In the last chapter we study binding of cationic peptides onto a lipid-bilayer membrane. The peptide not only interacts electrostatically with anionic lipids, rearranging their spatial distributions, but it can also insert hydrophobically into the membrane, expanding the area of its binding layer (i. e. , the outer layer). We examine how peptide charges and peptide insertion (thus area expansion) are intertwined. Our results show that, depending on the bilayer's surface charge density and peptide hydrophobicity, there is an optimal peptide charge yielding the maximum peptide penetration. Our results shed light on the physics behind the activity and selective toxicity of antimicrobial peptides, i. e. , they selectively rupture bacterial membranes while leaving host cells intact.

The ultrafast optical regime is defined, as it applies to laser pulses, along with a brief introduction to pulse generation and characterisation technologies. A more extensive description of our particular amplified pulse generation and SPIDER characterisation systems follows. Data verifying the correct operation of the characterisation system is presented and interpreted. Our laser system is then characterised in two different configurations. In each case, the data describing the system is presented and analyzed. Conclusions are made regarding the performance of both the characterisation and laser systems, along with suggested improvements for each.

In this thesis, based on the Onsager excluded volume interaction model, two nematic ordering problems of wormlike (semiflexible) polymer are studied: one is to investigate the isotropic-nematic interface of polymers for three typical cases&mdash;the flexible one, the rigid-rod one and the intermediate one; the other is to investigate a very long polymer confined between two infinite flat hard walls. <br /><br /> Many previous studies of the isotropic-nematic phase coexistence are mainly focused on either rigid rod-like polymers with small flexibility, or flexible polymers with large flexibility. The phase coexistence of polymers with intermediate flexibility is desired to be investigated. For these three typical cases (flexible, rigid-rod and intermediate), the profiles for density, order parameter and tension contribution were shown for different tilt angles. The interface tension was studied. The simulation results are consistent with those reported by other people. <br /><br /> We investigated the confinement of a long polymer between two flat hard walls, which are separated by a distance comparable to the effective Kuhn length of polymer chain by the wormlike chain model with or without the Onsager excluded volume interaction. Without the interaction, the results are compared with those of the Gaussian chain model. Including the interaction, the phase diagram is analyzed.

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. <br /><br /> Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden <em>SL</em>(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the <em>C</em>-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalizing the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalizations of Kaluza-Klein magnetic monopoles, generalizing the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalizing the known Reissner-Nordström solutions.