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Initial conditions in high-energy collisions
Year of Dissertation:
This thesis is focused on the initial stages of high-energy collisions in the saturation regime. We start by extending the McLerran-Venugopalan distribution of color sources in the initial wave-function of nuclei in heavy-ion collisions. We derive a fourth-order operator in the action and discuss its relevance for the description of color charge distributions in protons in high-energy experiments. We calculate the dipole scattering amplitude in proton-proton collisions with the quartic action and find an agreement with experimental data. We also obtain a modification to the fluctuation parameter of the negative binomial distribution of particle multiplicities in proton-proton experiments. The result implies an advancement of the fourth-order action towards Gaussian when the energy is increased. Finally, we calculate perturbatively the expectation value of the magnetic Wilson loop operator in the first moments of heavy-ion collisions. For the magnetic flux we obtain a first non-trivial term that is proportional to the square of the area of the loop. The result is close to numerical calculations for small area loops.
Ordering and topological defects in solids with quenched randomness
Year of Dissertation:
We explore multiple different examples of quenched randomness in systems with a continuous order parameter. In all these systems, it is shown that understanding the effects of topology is critical to the understanding of the effects of quenched randomness. We consider n-component fixed-length order parameter interacting with a weak random field in d=1,2,3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions have been studied on lattices containing hundreds of millions sites. At n-1d, when topological objects are absent, the final, lowest-energy, state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument. In the borderline case of n-1=d, when topological structures are non-singular, the system possesses a weak metastability with the Imry-Ma state likely to be the global energy minimum. We study random-field xy spin model at T=0 numerically on lattices of up to 1000x1000x1000 spins with the accent on the weak random field. Our numerical method is physically equivalent to slow cooling in which the system is gradually losing the energy and relaxing to an energy minimum. The system shows glass properties, the resulting spin states depending strongly on the initial conditions. Random initial condition for the spins leads to the vortex glass (VG) state with short-range spin-spin correlations defined by the average distance between vortex lines. Collinear and some other vortex-free initial conditions result in the vortex-free ferromagnetic (F) states that have a lower energy. The energy difference between the F and VG states correlates with vorticity of the VG state. Correlation functions in the F states agree with the Larkin-Imry-Ma theory at short distances. Hysteresis curves for weak random field are dominated by topologically stable spin walls raptured by vortex loops. We find no relaxation paths from the F, VG, or any other states to the hypothetical vortex-free state with zero magnetization. XY and Heisenberg spins, subjected to strong random fields acting at few points in space with concentration c_r << 1, are studied numerically on 3d lattices containing over four million sites. Glassy behavior with strong dependence on initial conditions is found. Beginning with a random initial orientation of spins, the system evolves into ferromagnetic domains inversely proportional to c_r in size. The area of the hysteresis loop, m(H), scales as c_r^2. These findings are explained by mapping the effect of strong dilute random field onto the effect of weak continuous random field. Our theory applies directly to ferromagnets with magnetic impurities, and is conceptually relevant to strongly pinned vortex lattices in superconductors and pinned charge density waves. The random-anisotropy Heisenberg model is numerically studied on lattices containing over ten million spins. The study is focused on hysteresis and metastability due to topological defects, and is relevant to magnetic properties of amorphous and sintered magnets. We are interested in the limit when ferromagnetic correlations extend beyond the size of the grain inside which the magnetic anisotropy axes are correlated. In that limit the coercive field computed numerically roughly scales as the fourth power of the random anisotropy strength and as the sixth power of the grain size. Theoretical arguments are presented that provide an explanation of numerical results. Our findings should be helpful for designing amorphous and nanosintered materials with desired magnetic properties.
PHASE SPACE EXPLORATIONS IN TIME DEPENDENT DENSITY FUNCTIONAL THEORY
Year of Dissertation:
Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated functional of the co-ordinate density, non-local in space and time. Adiabatic approximations (such as ALDA), which are local in time, are most commonly used in the increasing applications of the field. Going beyond ALDA, has been proved difficult leading to mathematical inconsistencies. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from two electron model systems. In this thesis work we propose a phase-space extension of the TDDFT. We want to answer the challenges the theory is facing currently by exploring the one-body phase-space. We give a general introduction to this theory iv and its mathematical background in the first chapter. In second chapter, we carryout a detailed study of instantaneous phase-space densities and argue that the functionals of distributions can be a better alternative to the nonlocality issue of the exchange-correlation potentials. For this we study in detail the interacting and the non-interacting phase-space distributions for Hookes atom model. The applicability of ALDA-based TDDFT for the dynamics in strongfields can become severely problematic due to the failure of single-Slater determinant picture.. In the third chapter, we analyze how the phase-space distributions can shine some light into this problem. We do a comparative study of Kohn-Sham and interacting phase-space and momentum distributions for single ionization and double ionization systems. Using a simple model of two-electron systems, we have showed that the momentum distribution computed directly from the exact KS system contains spurious oscillations: a non-classical description of the essentially classical two-electron dynamics. In Time dependent density matrix functional theory (TDDMFT), the evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be expressed in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. In v our fourth chapter, we show that by applying the quasi-classical and semiclassical approximations one can capture the natural occupations of the excited systems.We study a time-dependent Moshinsky atom model for this. The fifth chapter contains a comparative work on the existing non-local exchange-correlation kernels that are based on current density response frame work and the co-moving frame work. We show that the two approaches though coinciding with each other in linear response regime, actually turn out to be different in non-linear regime.
Non-linear response of 2D electron systems at low temperatures to electric and magnetic fields
Natalia Romero Kalmanovitz
Year of Dissertation:
The nonlinear behavior of low-dimensional electron systems has attracted a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. This work focuses on experimental results related to the nonlinear behavior of two dimensional electron systems. We first observed the non-linear zero-differential resistance state (ZDRS) that occurs for highly mobile two dimensional electron systems in response to a dc bias in the presence of a strong magnetic field applied perpendicular to the electron plane is suppressed. We found that it disappears gradually as the magnetic field is tilted away from the perpendicular at fixed filling factor. Good agreement is found with a model that considers the effect of the Zeeman splitting of Landau levels enhanced by the in-plane component of the magnetic field. Furthermore, we observed that when an electric field is applied to conductors, it heats electric charge carriers. It is demonstrated that an electric field applied to a conductor with a discrete electron spectrum produces a non-equilibrium electron distribution, which cannot be described by temperature. Such electron distribution changes significantly the conductivity of the electrons in a magnetic field, and forces them into a state with a zero differential resistance. Most importantly, the results demonstrate that in general, the effective overheating in the systems with discrete spectrum is significantly stronger than the one in systems with continuous and homogeneous distribution of the energy levels at the same input power. In the last part we observed non-linear behavior in a silicon MOSFET. Measurements of the rectification of microwave radiation at the boundary between two-dimensional electron systems separated by a narrow gap on a silicon surface for different temperatures, electron densities and microwave power, were performed. A theory is proposed that attributes the rectification to the thermoelectric response due to strong local overheating by the microwave radiation at the boundary between two dissimilar 2D metals.
Optical and Magneto-Optical Properties of type-II Excitons in ZnTe/ZnSe Stacked Submonolayer Quantum Dots
Year of Dissertation:
In this thesis we plan to develop understanding of the fundamental physical and material properties of type-II excitons in stacked ZnTe/ZnSe submonolayer quantum dots (QDs). The samples, grown via combination of molecular beam epitaxy (MBE) and migration enhanced epitaxy (MEE) are studied using photoluminescence (PL), time-resolved PL (TRPL) and PL in external magnetic field (Magneto-PL) as well as Magneto-TRPL. This thesis aims to discuss the key realizations keeping in mind the fundamental and advanced interests for such and related systems. In the first part of the thesis, effects of varying two crucial MBE growth parameters on the size and composition of the QDs are studied via detailed optical characterization with the goal of attaining better control over intentional growth. The second part of the thesis is focused on the magneto-optical studies, wherein observation of the optical excitonic Aharonov-Bohm (AB) effect in these type-II QD system has been discussed in details. The AB phase is revealed via the optical emission in magnetic field, observed as oscillation (AB `peak') in PL intensity. Presence of built-in electric field in the system is indicated from the narrow and robust AB oscillations. Detailed spectral analysis of the AB peak enabled us to determine lateral excitonic size with sub-nanometer precision as well as distinguish the presence of different QD stacks of the submonolayer QDs in the ensemble system. Magneto-time resolved PL measurements were performed to understand the influence of AB effect on the lifetime of magneto excitons due to transitions of angular momentum between optically "bright" and "dark" excitonic states. Our understandings have been discussed to the extent of the achieved results.
Variable Pressure Nuclear Magnetic Resonance Studies of Ionic Liquids and Electrophoretic Probe Design
Year of Dissertation:
Energy storage materials play a key role in, efficient, clean, and versatile use of energy, and are crucial for the exploitation of renewable energy. The improve efficiency of energy use stimulates the development of energy storage such as batteries or super capacitors, toward higher power and energy density, which significantly depends upon the advancement of new materials used in these devices. The new materials need better understanding and description in the electrochemical properties. Nuclear Magnetic Resonance (NMR) has been an important tool in the characterization of ionic liquids and solids. The measurements of the relaxation times and the diffusion coefficient are of great importance in understanding the dynamics at micro and macro scale and are performed as a function of temperature and pressure to obtain parameters such as activation energies and activation volumes respectively. In this work, studies of ionic liquids and polycarbonates are presented and the design and fabrication of cells used in the study of NMR under an electric field.
OPTOMECHANICS OF CAVITY DRIVEN NANOPARTICLES
Year of Dissertation:
The subject of this thesis is the opto-mechanical interaction of a spherical high-Q microresonator and a subwavelength particle, which, at optical wavelengths, corresponds to a size on the order of nanometers. After a review of the basic theory of spherical resonators and multi-sphere scattering, the full self-consistent electromagnetic field of the coupled resonator-particle system is derived. The particle-induced frequency shift and broadening is calculated by examining the poles of the scattering coefficients of the resonator. The force exerted on the particle by the field is determined via the Maxwell stress tensor, and is found to be in general non-conservative. From the force, the trajectories of the particle positioned outside the resonator are investigated. The relationship between frequency shift and the conservative and non-conservative components of the force is found to differ from the well-known formulas for the "gradient" and "scattering" force, which are commonly derived by neglecting the modification of the resonator field by the particle. The key aspects of this difference are investigated by re-deriving the results of the exact field calculations from a modified gradient/scattering framework, which explicitly takes into account the modification of the resonator field due to the particle.
Direct Growth of Graphene-like Films on Single Crystal Quartz Substrates
Year of Dissertation:
Direct growth of graphene-like (GL) films (nano-crystalline graphite films) on single crystal quartz substrates by chemical vapor deposition (CVD) from methane and molecular beam growth (MBG) is reported. The GL films have been characterized by means of Raman spectroscopy, atomic force microscopy and electrical measurements. Raman spectroscopy reveals nanocrystalline structure of the films grown at different conditions. The thinnest CVD grown GL films obtained so far have a thickness of 1.5 nm, a relatively rough surface structure and electrical conductivity in the range of 20 kohm/square. Low temperature Hall-effect measurements performed on these films have revealed that the major charge carriers are holes with mobility of 40 cm²/Vs at room temperature. While inferior to graphene in terms of electronic properties, the graphene-like films possess very high chemical sensitivity. Study of MBG grown films revealed formation of a non-conductive carbon layer of low crystallinity on the initial stage of the growth process. In order to study the influence of the quartz substrate on the film formation process we performed ab initio simulation of the MBG process. For this simulation we used an atom-by-atom approach, which, we believe, is a closer approximation to the real molecular beam deposition process reported so far. The simulation showed that the initial formation of the film follows the atomic structure of the substrate. This leads to a high content of sp3 hybridized atoms at the initial stage of growth and explains formation of a non-conductive film. Additionally, we demonstrated how a non-conductive film becomes conductive with the increase of the film thickness. These results agree fairly well with the data obtained by AFM, electrical, and Raman measurements conducted on the films grown by MBG. High chemical sensitivity of GL films has been demonstrated by measuring the change in their conductance during exposure to a NO2-containing atmosphere. Sensitivity of CVD grown GL films have been shown to be superior to that of MBG grown GL films. The stimulating action of ultraviolet light illumination on the chemical sensitivity has been found to be comparable to that of carbon nanotubes. A detection limit of 40 ppb (parts-per-billion) of NO2 diluted in an inert atmosphere has been estimated from the signal-to-noise ratio analysis. The optimal electrical conductance, high chemical sensitivity as well as the simple growth method make the CVD grown GL films promising for practical applications as a chemically sensitive material. Results obtained during this work were presented on several conferences: Gotham-Metro Condensed Matter Meeting (New York, NY), April 2010 and November 2012; American Physical Society March Meeting (Dallas, TX), March 2011; Nanoelectronic Devices for Defense & Security (NANO-DDS) Conference (Brooklyn, NY), August 2011. Two papers (http://dx.doi.org/10.1016/j.snb.2013.02.067 and http://dx.doi.org/10.1016/j.snb.2013.06.023) were published based on the results presented in this thesis.
Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes
Year of Dissertation:
The aim of this dissertation is threefold. We begin by the study of two parallel ideal cosmic strings in the presence of non-minimal scalar fields and spin- 1 gauge fields. We show that the contributions of the non-minimal term on the interaction energy between the strings are similar to that of the gauge field for a particular value of non-minimal coupling parameter. In this context we clarify some of the issues that arise when comparing the renormalization of black hole entropy and entanglement entropy using the replica trick. In the second part of the dissertation we study the process of bound state formation in clusters of Dp- brane collision and Dp shell/ Membrane collapse processes. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and timescale for formation of a bound state agree at the correspondence point, along with other relevant thermodynamic quantities. The timescale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity. Finally we study construction of local operators in AdS using the generalized AdS/ CFT correspondence. After briefly sketching previous works on this topic which involve massless and massive scalar fields, we present similar construction for spin- 1 and spin- 2 gauge fields. Working in holographic gauge in the bulk, at leading order in 1/N bulk gauge fields are obtained by smearing boundary currents over a sphere on the complexified boundary, while linearized metric fluctuations are obtained by smearing the boundary stress tensor over a ball. This representation respects AdS covariance up to a compensating gauge transformation. We also consider massive vector fields, where the bulk field is obtained by smearing a non-conserved current. We compute bulk two-point functions and show that bulk locality is respected. We show how to include interactions of massive vectors using 1/N perturbation theory, and we comment on the issue of general backgrounds. We point out some more recent works on interacting scalar and gauge fields and try to answer the question of what should be the CFT properties to have a dual gravitational descriptions on AdS space. We end with some speculations about finite N and when we have black holes in the bulk.
Performance Physics Analysis and Synthesis of Communicative Bodies
Year of Dissertation:
Human motion contains information like written or spoken language. Contemporary camera and computer technologies capture this information for gaming, animation, medical diagnostics and robotic control. In this thesis we model human performance recorded with motion capture and video. Beginning with a kinematic chain model of the human body we generate a metric for comparing different states of skeletal articulation. Applying this measure over motion data time series generates similarity spectra from which we identify and characterize body motions. We use the results to model the subject's underlying movement vocabulary with a network of connected recordings called a motion graph. We construct a set of motion graphs from video data and by assigning variable transition probabilities between recorded movement sequences we model the purposeful subject as a stochastic traversal process on the motion graph. Finally we present the application of a non-anatomical kinematic chain model to video data and derive the accompanying distance metrics. We discuss the results and possible applications of these techniques.