Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Quantum coherent phenomena in superconducting circuits and ultracold atoms(2010) Mitra, Kaushik; Lobb, Chris J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis consists of theoretical studies of superconducting qubits, and trapped bosons and fermions at ultracold temperature. In superconducting qubits I analyze the resonant properties and decoherence behavior of dc SQUID phase qubits, in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias lead. Typically qubit states in phase qubits are detected by tunneling it to the voltage state. I propose an alternate non-destructive readout mechanism which relies on the difference in the magnetic flux through the SQUID loop due to state of the qubit. I also study decoherence effects in a dc SQUID phase qubit caused by the isolation circuit. When the frequency of the qubit is at least two times larger than the resonance frequency of the isolation circuit, I find that the decoherence time of the qubit is two orders of magnitude larger than the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the isolation circuit. This theory is extended to other similar superconducting quantum devices and has been applied to experiments from the group at the University of Maryland. I also demonstrate, theoretically, vacuum Rabi oscillations, analogous to circuit-QED, in superconducting qubits coupled to an environment with resonance. The result obtained gives an exact analytical expression for coherent oscillation of state between the system (the qubit) and the environment with resonance. Next I investigate ultracold atoms in harmonically confined optical lattices. They exhibit a `wedding cake structure' of alternating Mott shells with different number of bosons per site. In regions between the Mott shells, a superfluid phase emerges at low temperatures which at higher temperatures becomes a normal Bose liquid. Using finite-temperature quantum field theoretic techniques, I find analytically the properties of the superfluid, Bose liquid, and Mott insulating regions. This includes the finite temperature order parameter equation for the superfluid phase, excitation spectrum, Berezinskii-Kosterlitz-Thouless transition temperature and vortex-antivortex pair formation (in the two dimensional case), finite temperature compressibility and density - density correlation function. I also study interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters I find emergence of superfluid and Fermi liquid (non-insulating) regions out of Bose-Mott and Fermi-band insulators, due to finite boson and fermion hopping. I also propose a possible experiment for the detection of superfluid and Fermi liquid shells through the use of Gauss-Laguerre and Gaussian beams followed by Bragg spectroscopy. Another area I explore is ultracold heteronuclear molecules such as KRb, RbCs and NaCs. I obtain the finite and zero-temperature phase diagram of bosons interacting via short range repulsive interactions and long-ranged isotropic dipolar interactions in two-dimensions. I build an analytical model for such systems that describes a first order quantum phase transition at zero temperature from a triangular crystalline phase (analogous to Wigner crystal phase of electrons) to superfluid phase. At finite temperature the crystalline phase melts, due to topological defects, to a hexatic phase where translational order is destroyed but hexagonal orientational order is preserved. Further temperature increase leads to the melting of the hexatic phase into a normal dipolar Bose liquid.Item PHENOMENOLOGY OF WARPED EXTRA DIMENSIONS(2010) Zhu, Lijun; Agashe, Kaustubh; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Warped extra dimensions provide a very interesting and attractive framework that solves the hierarchy problem of the Standard Model (SM) of particle physics through the curvature along an extra dimension. In this thesis I will discuss various aspects of collider phenomenology of warped extra dimensions. First, I will discuss a class of models within this framework that are very attractive due to their naturalness, which are called warped/composite Pseudo-Goldstone Boson (PGB) Higgs models. A generic prediction of these models is the existence of extra gauge bosons (called coset gauge bosons), which give rise to distinctive signatures at the Large Hadron Collider (LHC). However, due to the large masses (beyond 3 Teraelectronvolt (TeV)) of the coset gauge bosons and their small couplings to standard model states, their discovery would be very challenging at the LHC, and an upgrade of the LHC is needed. My second topic is about the phenomenology of the Higgs boson in warped extra dimensions. In models where fermions propagate in the extra dimension, there exist heavy excitations of SM fermions, which are called the Kaluza-Klein (KK) fermions. These KK states give sizable new contributions to the production and decay channels of the Higgs boson. I will give a detailed analysis of the Higgs boson couplings to massless vector bosons (gluons and photons) in warped extra dimensions. I will show that KK fermions of all generations contribute to these couplings, leading to significant deviation from the prediction of the SM. Therefore, precision measurement of the properties of the Higgs boson can shed light on the structure of warped extra dimensions even if KK particles cannot be directly produced at the LHC due to their heavy masses.Item Flavor Physics in the Models with Warped Extra Dimension(2010) Azatov, Aleksandr; Mohapatra, Rabindra N; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)I will first briefly review the Standard Model and gauge hierarchy problem. Then I will present the Randall-Sundrum model with warped extra dimension, which provides an elegant geometrical solution to the hierarchy problem. The main focus of this thesis will be an analysis of the flavor violation in the models with warped extra dimension. First I will discuss the bounds on the scale of the extra dimension arising from the low energy physics. I will show that there is a tension in the parameter space coming from different low energy observables, and I will also discuss possible ways to relax these bounds. Another interesting feature of the warped models is that they generically predict flavor violation in the Higgs sector. I will discuss low energy flavor constraints on the Higgs mediated flavor violation as well as its signatures at the collider experiments. In the last part of this thesis I will discuss the physics of radion, a scalar degree of freedom of the five dimensional gravity multiplet, and I will show why it has interactions which are generically flavor misaligned leading to the observable flavor violation. This, combined with the fact that radion is likely to be the lightest new physics degree of freedom will lead to the interesting phenomenology both from perspective of collider phenomenology and low energy observables.Item Topics in Lattice QCD and Effective Field Theory(2010) Buchoff, Michael Ireland; Bedaque, Paulo F; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (χPT ), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice χPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 ππ scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.Item Controlling Molecular-Scale Motion: Exact Predictions for Driven Stochastic Systems(2010) Horowitz, Jordan Michael; Jarzynski, Christopher; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Despite inherent randomness and thermal fluctuations, controllable molecular devices or molecular machines are currently being synthesized around the world. Many of these molecular complexes are non-autonomous in that they are manipulated by external stimuli. As these devices become more sophisticated, the need for a theoretical framework to describe them becomes more important. Many non-autonomous molecular machines are modeled as stochastic pumps: stochastic systems that are driven by time-dependent perturbations. A number of exact theoretical predictions have been made recently describing how stochastic pumps respond to arbitrary driving. This work investigates one such prediction, the current decomposition formula, and its consequences. The current decomposition formula is a theoretical formula that describes how stochastic systems respond to non-adiabatic time-dependent perturbations. This formula is derived for discrete stochastic pumps modeled as continuous-time Markov chains, as well as continuous stochastic pumps described as one-dimensional diffusions. In addition, a number of interesting consequences following from the current decomposition formula are reported. For stochastic pumps driven adiabatically (slowly), their response can be given a purely geometric interpretation. The geometric nature of adiabatic pumping is then exploited to develop a method for controlling non-autonomous molecular machines. As a second consequence of the current decomposition formula, a no-pumping theorem is proved which provides conditions for which stochastic pumps with detailed balance exhibit no net directed motion in response to non-adiabatic cyclic driving. This no-pumping theorem provides an explanation of experimental observations made on 2- and 3-catenanes.Item A Continuum Model for Flocking: Obstacle Avoidance, Equilibrium, and Stability(2010) Mecholsky, Nicholas Alexander; Ott, Edward; Antonsen, Jr., Thomas M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention. In this dissertation, we present a partial-differential-equation based continuum model of flocking and use it to investigate several properties of group dynamics and equilibrium. We analyze the reaction of a flock to an obstacle or an attacking predator. We show that the flock response is in the form of density disturbances that resemble Mach cones whose configuration is determined by the anisotropic propagation of waves through the flock. We investigate the effect of a flock `pressure' and pairwise repulsion on an equilibrium density distribution. We investigate both linear and nonlinear pressures, look at the convergence to a ‘cold’ (T → 0) equilibrium solution, and find regions of parameter space where different models produce the same equilibrium. Finally, we analyze the stability of an equilibrium density distribution to long-wavelength perturbations. Analytic results for the stability of a constant density solution as well as stability regimes for constant density solutions to the equilibrium equations are presented.Item Dispersion of ion gyrocenters in models of anisotropic plasma turbulence(2009) Gustafson, Kyle Bergin; Dorland, William D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Turbulent dispersion of ion gyrocenters in a magnetized plasma is studied in the context of a stochastic Hamiltonian transport model and nonlinear, self-consistent gyrokinetic simulations. The Hamiltonian model consists of a superposition of drift waves derived from the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. Finite Larmor radius (FLR) effects are included. Because there is no particle transport in the direction of the density gradient, the focus is on transport parallel to the shear flow. The prescribed flow produces strongly asymmetric non-Gaussian probability distribution functions (PDFs) of particle displacements, as was previously known. For kρ=0, where k is the characteristic wavelength of the flow and ρ is the thermal Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. The transition separates nearly ballistic superdiffusive dispersion from weaker superdiffusion at later times. FLR effects eliminate this transition. Important features of the PDFs of displacements are reproduced accurately with a fractional diffusion model. The gyroaveraged ExB drift dispersion of a sample of tracer ions is also examined in a two-dimensional, nonlinear, self-consistent gyrokinetic particle-in-cell (PIC) simulation. Turbulence in the simulation is driven by a density gradient and magnetic curvature, resulting in the unstable ρ scale kinetic entropy mode. The dependence of dispersion in both the axial and radial directions is characterized by displacement and velocity increment distributions. The strength of the density gradient is varied, using the local approximation, in three separate trials. A filtering procedure is used to separate trajectories according to whether they were caught in an eddy during a set observation time. Axial displacements are compared to results from the Hasegawa-Mima model. Superdiffusion and ballistic transport are found, depending on filtering and strength of the gradient. The radial dispersion of particles, as measured by the variance of tracer displacements, is diffusive. The dependence of the running diffusion coefficient on ρ for each value of the density gradient is considered.Item Scattering from chaotic cavities: Exploring the random coupling model in the time and frequency domains(2009) Hart, James Aamodt; Ott, Edward; Antonsen, Thomas M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Scattering waves off resonant structures, with the waves coupling into and out of the structure at a finite number of locations (`ports'), is an extremely common problem both in theory and in real-world applications. In practice, solving for the scattering properties of a particular complex structure is extremely difficult and, in real-world applications, often impractical. In particular, if the wavelength of the incident wave is short compared to the structure size, and the dynamics of the ray trajectories within the scattering region are chaotic, the scattering properties of the cavity will be extremely sensitive to small perturbations. Thus, mathematical models have been developed which attempt to determine the statistical, rather than specific, properties of such systems. One such model is the Random Coupling Model. The Random Coupling Model was developed primarily in the frequency domain. In the first part of this dissertation, we explore the implications of the Random Coupling Model in the time domain, with emphasis on the time-domain behavior of the power radiated from a single-port lossless cavity after the cavity has been excited by a short initial external pulse. In particular, we find that for times much larger than the cavity's Heisenberg time (the inverse of the average spacing between cavity resonant frequencies), the power from a single cavity decays as a power law in time, following the decay rate of the ensemble average, but eventually transitions into an exponential decay as a single mode in the cavity dominates the decay. We find that this transition from power-law to exponential decay depends only on the shape of the incident pulse and a normalized time. In the second part of this dissertation, we extend the Random Coupling Model to include a broader range of situations. Previously, the Random Coupling Model applied only to ensembles of scattering data obtained over a sufficiently large spread in frequency or sufficiently different ensemble of configurations. We find that by using the Poisson Kernel, it is possible to obtain meaningful results applicable to situations which vary much less radically in configuration and frequency. We find that it is possible to obtain universal statistics by redefining the radiation impedance parameter of the previously developed Random Coupling Model to include the average effects of certain classical trajectories within the resonant structure. We test these results numerically and find good agreement between theory and simulation.Item Transport in Poygonal Billiard Systems(2009) Reames, Matthew Lee; Dorfman, J. R.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The aim of this work is to explore the connections between chaos and diffusion by examining the properties of particle motion in non-chaotic systems. To this end, particle transport and diffusion are studied for point particles moving in systems with fixed polygonal scatterers of four types: (i) a periodic lattice containing many-sided polygonal scatterers; (ii) a periodic lattice containing few-sided polygonal scatterers; (iii) a periodic lattice containing randomly oriented polygonal scatterers; and (iv) a periodic lattice containing polygonal scatterers with irrational angles. The motion of a point particle in each of these system is non-chaotic, with Lyapunov exponents strictly equal to zero.Item Non-linear Development of Streaming Instabilities in Magnetic Reconnection with a Strong Guide Field(2009) Che, Haihong; Drake, James F.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Magnetic reconnection is recognized as a dominant mechanism for converting magnetic energy into the convective and thermal energy of particles, and the driver of explosive events in nature and laboratory. Magnetic reconnection is often modeled using resistive magnetohydrodynamics, in which collisions play the key role in facilitating the release of energy in the explosive events. However, in space plasma the collisional resistivity is far below the required resistivity to explain the observed energy release rate. Turbulence is common in plasmas and the anomalous resistivity induced by the turbulence has been proposed as a mechanism for breaking the frozen-in condition in magnetic reconnection. Turbulence-driven resistivity has remained a poorly understood, but widely invoked mechanism for nearly 50 years. The goal of this project is to understand what role anomalous resistivity plays in fast magnetic reconnection. Turbulence has been observed in the intense current layers that develop during magnetic reconnection in the Earth's magnetosphere. Electron streaming is believed to be the source of this turbulence. Using kinetic theory and 3D particle-in-cell simulations, we study the nonlinear development of streaming instabilities in 3D magnetic reconnection with a strong guide field. Early in time an intense current sheet develops around the x-line and drives the Buneman instability. Electron holes, which are bipolar spatial localized electric field structures, form and then self-destruct creating a region of strong turbulence around the x-line. At late time turbulence with a characteristic frequency in the lower hybrid range also develops, leading to a very complex mix of interactions. The difficulty we face in this project is how to address a long-standing problem in nonlinear kinetic theory: how to treat large amplitude perturbations and the associated strong wave-particle interactions. In my thesis, I address this long-standing problem using particle-in-cell simulations and linear kinetic theory.Some important physics have been revealed. 1: The lower hybrid instability (LHI) dominates the dynamics in low $beta$ plasma in combination with either the electron-electron two-stream instability (ETS) or the Buneman instability (BI), depending on the parallel phase speed of the LHI. 2: An instability with a high phase speed is required to tap the energy of the high velocity electrons. The BI with its low phase speed, can not do this. The ETS and the LHI both have high phase speed. 3: The condition for the formation of stable electron holes requires $|v_p -v_g|< sqrt{2e|phi|/m_e}$, where $|phi|$ is the amplitude of the electric potential, and $v_p$ and $v_g$ are the phase and group velocity of the relevant waves. Like ETS and BI, LHI all can form electron holes. 4: The overlapping resonance in phase space is the dominant mechanism for transporting the momentum and energy from high velocity electrons to low velocity electrons, which then couple to the ions.
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