Despite the great successes of the Cold Dark Matter (CDM) model in explaining a wide range of observations of the global evolution and the formation of galaxies and large-scale structure in the universe, the origin and microscopic nature of this dark matter is still unknown. The most common form of CDM considered to-date is that of Weakly Interacting Massive Particles (WIMPs), but some of the cosmological predictions for this kind of CDM are in apparent conflict with observations (e.g. cuspy-cored halos and an overabundance of satellite dwarf galaxies). For these reasons, it is important to consider the consequences of different forms of CDM. We focus here on the hypothesis that the dark matter is comprised, instead, of ultralight bosons that form a Bose-Einstein Condensate (BEC), described by a complex scalar field. We start from the Klein-Gordon and Einstein field equations to describe the evolution of the Friedmann-Robertson-Walker (FRW) universe in the presence of this kind of dark matter. We find that, in addition to the phases of radiation-domination (RD), matter-domination (MD) and Lambda-domination (LD) familiar from the standard CDM model, there is an earlier phase of scalar-field-domination (SFD) which is special to this model. In addition, while WIMP CDM is non-relativistic at all times after it decouples, the equation of state of BEC-SFDM is found to be relativistic at early times, evolving from incompressible ($\bar{p} = \bar{\rho}$) to radiation-like ($\bar{p} = \bar{\rho}/3$), before it becomes non-relativistic and CDM-like at late times. The timing of the transitions between these phases and regimes is shown to yield fundamental constraints on the particle mass and self-interaction coupling strength. We also discuss progress on the description of structure formation in this model, which includes additional constraints on these parameters. / text

Topological insulators(TIs) constitute a novel state of quantum matter which possesses non-trivial topological properties. Although discovered only in the recent few years, TIs have attracted intensive interest among the community of condensed matter physics and material science. TIs are insulating in the bulk but have conductive gapless edge or surface states on the boundaries, which have their origin in the nontrivial bulk band topology that is induced by the strong spin-orbital interactions in the materials. Existing in all dimensions, TIs exhibit a variety of exotic physics such as quantum spin Hall effect, momentum-spin locked surface states, Dirac fermion transport, quantized anomalous Hall effect, Majorana fermions, etc. In this thesis, I study the transport properties of 2D and 3D TIs by numerical approaches. As an introduction, a brief review of TIs is given. A detailed description of the numerical methods is also presented. The results can be summarized in four aspects. First, disorder is found be able to induce a non-trivial TI from an originally trivial band insulator, where the conductance of a two terminal device drops to nearly zero and then rises to form an anomalous plateau as disorder strength is increased, and finally all the states become localized. The real space Chern number calculation as well as the effective medium theory suggests that disorder is fundamentally responsible for the emerging of the extended helical edge states in this system. We also present a levitation and pair annihilation picture of the extended states for this model. Second, by making the 2D TIs into singly connected quantum point contacts(QPCs), I show a coherent and fast Aharonov-Bohm oscillation of conductance caused by the quantum interference of the helical edge states. This oscillation not only happens against weak magnetic field but also against the gate voltage in the zero-field condition. This results in a giant edge magnetoresistance of the device in weak magnetic fields. The amplitude of the magnetoresistance is controllable by adjusting either the QPCs' slit width or the interference loop size in the device. The oscillation is found robust against disorder. Third, by applying a uniform spin-splitting Zeeman field in the bulk of the 3D TI whose surface states can be viewed as massless Dirac fermions, I find chiral edge states on the gapped surfaces of the 3D TI, which can be considered as interface states between domains of massive and massless Dirac fermions. Effectively these states are result of splitting of a perfect interface conducting channel. This picture is confirmed by the Landauer-B?ttiker calculations in four-terminal Hall bars. Finally, I propose the concept of topological semi-metals. By calculating the local density of states on the surfaces, I demonstrate that surface states and the gapless Dirac cone already exist in the system although the bulk is not gapped. We show how the uni-axial strain induces an insulating band gap and turn the semi-metal into true TI. We predict existence of quantum spin Hall effect in the thin films made of these materials, which can be significantly enhanced by disorders. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

Evolved stars including asymptotic giant branch stars, proto-planetary nebulae and planetary nebulae are well known to be sources of molecules for the interstellar medium. Circumstellar envelopes of asymptotic giant branch stars are known to be sites of active molecular synthesis. These molecular species are then distributed to the interstellar medium as the envelope is gradually ejected in the proto-planetary nebula and planetary nebula phases. As carbon that is dredged-up from the stellar core by convectional instabilities facilitates rapid formation and reprocessing of molecules, the chemical abundances differ significantly between objects at different stages of stellar evolution. Changes in the physical conditions in the envelope also allow different chemical processes to take place throughout the evolutionary sequence. Conducting spectral line surveys on a large sample of objects at different stages of stellar evolution will allow one to track those chemical and physical changes along the evolutionary track. Presented in this thesis are the results from a series of unbiased systematic line surveys targeting the circumstellar envelopes of evolved stars. As part of an on-going effort, these surveys aim to expand the coverage both in terms of objects at different evolutionary stages and wavelength ranges in order to paint a more complete picture in our understanding of the chemical evolution in objects at the final stages of stellar evolution. All surveys included in the present study are conducted using the 45m radio telescope at the Nobeyama Radio Observatory, and the same instrumental settings were used when observing a given frequency region to minimize the systematic uncertainties. The four objects surveyed in this study, the asymptotic giant branch star CIT6, the proto-planetary nebulae CRL 2688 and CRL 618, and the planetary nebula NGC7027, represent a healthy sample from all key phases of late-stage stellar evolution. Since the surveys are conducted in millimeter-wavelengths, they are mostly targeting rotational transitions from molecules. In particular, rotational transitions associated with the cyanopolyyne chain HC7N reported in the survey of CIT6 and CRL 2688 are novel detections. Spectra from the series of surveys are analyzed using previously obtained spectra of the prototypical asymptotic giant branch star IRC+10216 as a benchmark. Results from fractional abundance computations suggested that CIT6 is a more evolved specimen relative to IRC+10216 and supported chemical models pertaining to the synthesis of cyanopolyyne chains. Intensity ratios in CRL 2688 showed that the cyanopolyyne enrichment towards conclusion of the asymptotic giant branch phase is no longer present in proto-planetary nebulae. Rotational analysis provided evidence to support the hypothesis that the ammonia absorption in CRL 618 originates from two distinct components. Flux ratios in NGC7027 also showed that the recombination lines in the planetary nebula behave according to theoretical predictions. Altogether, these findings will complement previous results and enable one to trace and understand the interplay between chemistry and physical conditions within the circumstellar envelope as objects proceeds on the evolutionary track. / published_or_final_version / Physics / Master / Master of Philosophy

Although a number of methods with appropriate approximations, such as mean-field theory, local density approximation, and tight-binding method have been well developed and widely used in solid state physics, they possess strong limitations, and thus physicists never stop trying to find methods that could rigorously solve the models of condensed matter systems. This thesis presents several new exact solutions for electron pairing models with spin-orbit interactions and Zeeman coupling, which have not been studied before. First, a type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson’s previous work for 2D cases. Based on the exact solutions for the electron pairing model with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p+ip wave and the ground state possesses time-reversal symmetry, which are expected by the meanfield theory. And the difference is that such peroration from our framework is valid for any strength of the pairing interactions. Intriguingly, how Majorana fermions can emerge is also elaborated in a ribbon system as well. Condensation energy and critical magnetic field are calculated in two systems with the exact solutions, and compared with the relevant results achieved by the mean-field theory, the differences between our results and the mean-field theory show the significance of the work for exact solutions. Secondly, we generalize our scenario to 3D cases. Several remarks of the 3D case are given following the significant results from the 2D cases. And an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov ground state is revealed exactly, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. As a by-product, a similar Fulde-Ferrel-Larkin-Ovchinnikov state is also disclosed when the magnetic field is in the same plane of k for 2D case. In addition, applying the transformative Richardson ansatz in bosonic system, we elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensed matter as well. Finally, we discuss the application of the exact solutions in quantum entanglement quantification. The entanglement monotone concurrence is calculated with exact solutions for two models. It is found to be a smooth function of pairing interactions, as expected. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

In recent years, studies of diffusion in random media have been extended to include the effects of media in which the defects fluctuate randomly in time. Typically, the diffusive motion of particles in a static medium persists when the medium is allowed to fluctuate, with the diffusivity (diffusion constant) D depending on the character of the fluctuations. In the present work, we study random walks on lattices in which the bonds connecting vertices open and close randomly in time, and the walker is not allowed to cross a closed bond. Variations of the model studied here have been used to model the diffusion of CO through myoglobin, the transport of ions in polymer solutions, and conduction in hydrogenated amorphous silicon. The major objective in analyzing these systems is to find efficient methods for computing the diffusivity. In this dissertation, we focus mainly on methods of computing the diffusivity in our model. In addition, we study the critical behavior of the model and present a demonstration, valid for a restricted range of model parameters, that the distribution of the displacement converges in time to a Gaussian with width D. To compute the diffusivity, we use a numerical renormalization group (RG) method, power series expansions in model parameters, and Monte Carlo simulations. We choose a model with two parameters characterizing the bond fluctuations--the time scale of fluctuations tau and the mean open-bond density p. We calculate a series expansion of the diffusivity to about 10th order in the parameter nu = exp(.1/τ) on the hypercubic lattice Zᵈ for d = 1, 2, 3, as well as on the Bethe lattice. We compute the same power series expansion to 3rd order in ν for arbitrary d. We compute estimates of the diffusivity on the Bethe lattice using the RG methods and show by comparison to Monte Carlo data that the RG provides excellent quantitative predictions of D when τ is not too large.

<p>We are interested in the transition from an amorphous material to a polycrystalline structure. Previous research done by our group introduced a modified Random Nucleation and Growth model to describe this phenomenon. Besides the nucleation rate, its importance in the grain size distribution (GSD) having long been established, we introduced an effective time dependent growth rate, postulated the analytic form, and ascertained its effect on the GSD to match experimental data. Not only would we like to continue to substantiate this form, we wish also to determine how this rate depends on the fundamental parameters of the model. To achieve this, we have developed a numerical simulation in two dimensions, based on the premises of the model, to simulate crystallization in thin films. Not only does the simulation produce data that matches the analytical results of the nucleation rate and volume fraction available for nucleation, it also fits well with the postulated growth rate. This suggests the validity of the introduced effective growth rate and the functionality of the simulation for studying this process. </p>

The rapid progress of the field of ultracold atoms during the past two decades has set new milestones in our control over matter. By cooling dilute atomic gases and molecules to nano-Kelvin temperatures, novel quantum mechanical states of matter can be realized and studied on a table-top experimental setup while bulk matter can be tailored to faithfully simulate abstract theoretical models. Two of such models which have witnessed significant experimental and theoretical attention are (1) the two-component Fermi gas with resonant $s$-wave interactions, and (2) the single-component Fermi gas with dipole-dipole interactions. This thesis is devoted to studying the non-equilibrium collective dynamics of these systems using the general framework of quantum kinetic theory. / Physics

The fractional quantum Hall effect occurs when an extremely clean 2-dimensional fermion gas is subject to a magnetic field. This simple set of circumstances creates phenomena, such as edge reconstruction and fractional statistics, that remain subjects of experimental study 30 years after the discovery of the fractional quantum Hall effect. This thesis investigates the properties of excitations of the fractional quantum / Physics

published_or_final_version / abstract / toc / Physics / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy