Disorder can have a vast variety of consequences for the physics of phase transitions. Some transitions remain unchanged in the presence of disorder while others are completely destroyed. In this dissertation we study the effects of quenched disorder on electronic systmens at zero temperature. First, we perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g* signaling the crossover to strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects. Second, we formulate a strong-disorder renormalization-group (SDRG) approach to study the beta function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the band center. We show that the SDRG method, when used to compute transport properties, yields exact results since it is identical to the transfer matrix method. The beta function is shown to be universal when only off-diagonal disorder is present even though single-parameter scaling is known to be violated. A different single-parameter scaling theory is formulated for this particular (particle-hole symmetric) case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the beta function is shown to crossover from the universal behavior of the particle-hole symmetric case to the conventional nonuniversal one in agreement with the two-parameter scaling theory. We finally draw an analogy with the random transverse-field Ising chain in the paramagnetic phase. The particle-hole symmetric case corresponds to the critical point of the quantum Ising model, while the generic case corresponds to the Griffiths paramagnetic phase. Finally, we implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos- Renyi random graphs, which represent an appropriate infinite dimensional limit. Our SDRG algorithm is based on a judicious elimination of most (irrelevant) new bonds generated under RG. It yields excellent agreement with exact numerical results for universal properties at the critical point without significant increase of computer time, and confirm that, for Anderson localization, the upper critical dimension duc = infinite. We find excellent convergence of the relevant 1/d expansion down to d = 2, in contrast to the conventional 2 + ε expansion, which has little to say about what happens in any d [greater than] 3. We show that the mysterious mirror symmetry of the conductance scaling function is a genuine strong-coupling effect, as speculated in early work. This opens an efficient avenue to explore the critical properties of Anderson transition in the strong-coupling limit in high dimensions. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / November 4, 2015. / Anderson transition, disordered systems, finite size scaling, random, Renormalziation Group, SDRG / Includes bibliographical references. / Vladimir Dobrosavljević, Professor Directing Dissertation; Vincent J. M. Salters, University Representative; Stephan von Molnar, Committee Member; Kun Yang, Committee Member; Jorge Piekarewicz, Committee Member.

Three doping studies on Kondo lattices are investigated in this thesis: FeSi1-xGex, Ce1-xLaxCoIn5, and Yb1-xYxInCu4. For FeSi1-xGex, we constructed the phase diagram through the analysis of magnetic, thermal and transport measurements on single crystals. The phase diagram shows a first-order transition from a Kondo insulator (exponentially activated properties) to a ferromagnetic metal at a critical concentration, xc ~ 0:25. The field dependence of the magnetization (M(H)) shows that the saturation moment of x = 0:27 is 10 times larger than that of x = 0:24. The spin gap of x = 0:24, 167K, is quite close to the transition temperature of x = 0:27, 150K, indicating that the characteristic energies of the two competing phases, i.e. the Curie temperature and the spin gap of the Kondo insulator, are essentially equal at the critical concentration. For x c, spin gap, transport gap and resistivity minimum systematically decrease with increasing x. Saturation moments and specific heat coefficients are almost zero for x c. The temperature dependence of magnetic susceptibility (X(T)) for x = 0:2 shows a broad maximum around 200K, indicating that the broad maximum temperature decreases with x for x c. The variable range hopping analysis suggests the existence of the localized state for this region. For x > x xc, the data break into two distinct regimes: xc» 0:5 and » 0:5 · 1. For xc 0:5, X(T) does not displays a sharp transition at Tc and M(H) increases with increasing fields. The temperature dependence of the resistivity (ρ(T)) shows metallic behavior. However, it does not have any kink at Tc. In contrast, for ~ 0:5 · 1, X(T) displays a sharp transition at Tc and M(H) saturates at H ~ 0:3T. ρ (T) has a kink at Tc. Based on the Kondo insulator picture, we can explain the specific heat coefficient y evolution with x. The transition from a Kondo insulator to a ferromagnetic metal can be explained as the consequence of the changes in hybridization between Fe 3d electrons and Si/Ge p conduction electrons in conjunction with disorder on the Si/Ge ligand site. For Ce1-xLaxCoIn5, we studied antiferromagnetic intersite correlations for the Kondo lattice by comparison with data on the single Kondo impurity. All the magnetic susceptibility per mole Ce for H || ab plane and H || c axis collapse onto one curve above 100K in Ce1-xLaxCoIn5, indicating the same high T Kondo temperature (~ 35K) for all concentrations. Further, the magnetic part of the resistivity shows the same -logT dependence above 50K for all concentrations, again indicating that the high T Kondo temperature is essentially independent of Ce concentration. The magnetic part of the heat capacity for Ce1-xLaxCoIn5 alloys has a peak around 70K, suggesting the same crystalline field splittings occurs the alloy series Ce1-xLaxCoIn5. Based on these experimental findings, the scaling laws for the susceptibility and the heat capacity reveal that the screening of the magnetic moments in this Kondo lattice involves antiferromagnetic intersite correlations and this intersite correlation has a larger energy scale compared to the Kondo impurity case. In addition, a Fermi liquid ground state appears in the La rich region while the specific heat and inelastic part of ρm show non-Fermi liquid behavior for Ce rich region. For Yb1-xYxInCu4, measurements using cantilever torque magnetometry discover the new phase above Hv for x = 0 and x = 0:1. With proper scaling of the critical fields and temperatures, data for all alloys collapse onto the same curve, representing a common phase above Hv. The magneto-resistance does not change at the new phase boundary. Due to the crystalline electric field, there is anisotropy of the valence transition in applied magnetic field in different directions. For x = 0:2, the specific heat and the resistance indicate the appearance of a spin glass state below 4K for H > 5T. Since Ytterbium occupies the corners of a tetrahedron in the F43m structure, the spin glass state is not unexpected. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2003. / Date of Defense: November 4, 2003. / Kondo Lattice, Mixed Valence State, Kondo Insulator, Heavy Fermion Superconductor / Includes bibliographical references. / Zachary Fisk, Professor Directing Dissertation; Naresh Dalal, Outside Committee Member; Stephan von Molnar, Committee Member; Nicholas Bonesteel, Committee Member; Jorge Piekarewicz, Committee Member.

Proteins are flexible and dynamic. One static structure alone does not often completely explain biological functions of the protein, and some proteins do not even have high resolution structures. In order to provide better understanding to the biological functions of nicotinic acetylcholine receptor, Diphtheria toxin repressor and M2 proton channel, the dynamics of these proteins are investigated using molecular modeling and molecular dynamics (MD) simulations. With absence of high resolution structure of alpha 7 receptor, the homology models of apo and cobra toxin bound forms have been built. From the MD simulations of these model structures, we observed one subunit of apo simulation moved away from other four subunits. With local movement of flexible loop regions, the whole subunit tilted clockwise. These conformational changes occurred spontaneously, and were strongly correlated with the conformational change when the channel is activated by agonists. Unlike other computational studies, we directly compared our model of open conformation with the experimental data. However, the subunits of toxin bound form were stable, and conformational change is restricted by the bound cobra toxin. These results provide activation and inhibition mechanisms of alpha 7 receptors and a possible explanation for intermediate conductance of the channel. Intramolecular complex of SH3-like domain with a proline-rich (Pr) peptide segment in Diphtheria toxin repressor (DtxR) is stabilized in inactive state. Upon activation of DtxR by transition metal binding, this intramolecular complex should be dissociated. The dynamics of this intramolecular complex is investigated using MD simulations and NMR spectroscopy. We observed spontaneous opening and closing motions of the Pr segment binding pockets in both Pr-SH3 and SH3 simulations. The MD simulation results and NMR relaxation data suggest that the Pr segment exhibits a binding ¡ê unbinding equilibrium. Despite a wealth of experimental validation of Gouy-Chapman (GC) theory to charged lipid membranes, a test of GC theory by MD simulations has been elusive. Here we demonstrate that the ion distributions at different salt concentrations in anionic lipid bilayer systems agree well with GC predictions using MD simulations. Na+ ions are adsorbed to the bilayer through favorable interactions with carbonyls and hydroxyls, reducing the surface charge density by 72.5%. The interactions of amantadine, an antiinfluenza A drug, with DMPC bilayers are investigated by an MD simulation and by solid-state NMR. The MD simulation results and NMR data demonstrate that amantadine is located within the interfacial region with upward orientation and interacts with the lipid headgroup and glycerol backbone, while the adamantane group of amantadine interacts with the glycerol backbone and much of fatty acyl chain, as it wraps underneath of the drug. The lipid headgroup orientation is influenced by the drug as well. The recent prevalence of amantadine-resistant mutants makes a development of new drug urgent. The mechanism of inhibition of M2 proton channel in influenza virus A by amantadine is investigated. In the absence of high resolution structure, we model the apo and drug bound forms based on NMR structures. MD simulations demonstrate that channel pore is blocked by a primary gate formed by Trp41 helped by His37 and a secondary gate formed by Val27. The blockage by the secondary gate is extended by the drug bound just below the gate, resulting in a broken water wire throughout the simulation, suggesting a novel role of Val27 in the inhibition by amantadine. Recent X-ray structure validates the simulation results. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2008. / Date of Defense: April 28, 2008. / Molecular Biophysics, Computational Biophysics, Membrane Protein, Spontaneous Conformational Change, Molecular Modeling, Molecular Dynamics Simulation, Protein Dynamics, Ligand Binding, Drug Design / Includes bibliographical references. / Huan-xiang Zhou, Professor Directing Dissertation; Timothy M. Logan, Outside Committee Member; Bernd A. Berg, Committee Member; Peng Xiong, Committee Member; Hugh Nymeyer, Committee Member.

High-energy heavy-ion collisions are a powerful tool in the laboratory to investigate the phase transition from ordinary nuclear matter to a deconfined state of quarks and gluons, called the Quark-Gluon Plasma (QGP), which is predicted to be formed above a temperature of order Tc ~ 170 MeV in lattice Quantum Chromodynamics (QCD). Suppression of J/ψ production has long been considered to be one of the most promising signatures for the deconfinement of matter. J/ψ production has been measured by the PHENIX experiment, one of the two major experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) in p + p, d + Au, Au + Au and Cu + Cu collisions at the center of mass energy per nucleon (√sNN) of 200 GeV. The analysis of the Cu + Cu data is the focus of this dissertation. Yields of J/Psi production in Cu + Cu collisions at √sNN = 200 GeV have been measured by the PHENIX experiment over the rapidity range |y| / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2008. / Date of Defense: April 7, 2008. / Heavy-Ion Collisions, J/Psi, Nuclear Physics / Includes bibliographical references. / Volker Crede, Professor Directing Dissertation; Sanford Safron, Outside Committee Member; Anthony D. Frawley, Committee Member; Simon Capstick, Committee Member; Howie Baer, Committee Member.

The study of baryon resonances offers a deeper understanding of the strong interaction, since the dynamics and relevant degrees of freedom hidden within them are reflected by the properties of these states. The baryon resonances have been fairly accurately predicted in the low-energy region by constituent quark models and lattice quantum chromodynamics. However, most of the predicted higher-lying excited resonances (center-of-mass energies above 1.7 GeV/c²) and experimental findings do not match up. The model calculations predict more baryon resonances than have been experimentally observed. Quark model calculations have suggested that some of the unobserved resonances couple strongly to γp reactions. The higher-lying excited are also generally predicted to have strong couplings to final states involving a heavier meson, e.g. one of the vector mesons, ρ, ω, ϕ. The excited states of the nucleon are usually found as broadly overlapping resonances, which may decay into a multitude of finasl states involving mesons and baryons. Polarization observables make it possible to isolate singleresonance contributions from other interference terms. This works presents measurements of the helicity asymmetry, E, for the reaction γp → pω in the energy range 1.1 GeV < Eγ < 2.3 GeV, differential cross sections, and spin density matrix elements, also for the reaction γp → pω in the energy range 1.5 GeV < Eγ < 5.4 GeV. Photoproduction of nucleon resonances in their decay to strange particles also offers attractive possibilities because the strange quark in the particle generates another degree of freedom and gives additional information not available from the nucleon-nucleon scattering. Thus, we have also extracted the helicity asymmetry, E, for the reaction γp → K⁰Σ⁺ in the energy range 1.1 GeV < Eγ < 2.1 GeV, differential cross sections, and recoil hyperon polarization, P, also for the reaction γp → K⁰Σ⁺ in the energy range 1.15 GeV < Eγ < 3.0 GeV. The data were collected at Jefferson Lab, using the CLAS detector, as part of the g9a and g12 experiments. Both experiments, as part of the N* spectroscopy program at Jefferson Laboratory, accumulated photoproduction data using circularly-polarized photons incident on a longitudinally-polarized butanol target in the g9a experiment and un-polarized liquid hydrogen target for the g12 experiment. A partial-wave analysis to the E data for the reaction γp → pω within the Bonn-Gatchina framework found dominant contributions from the 3/2⁺ near threshold, which is identified with the sub-treshold N(1720)3/2⁺ resonance. Some additional resonances and the t-channel π and pomeron exchange are needed to describe the data. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / July 10, 2018. / CLAS detector, Hadronic Physics, Jefferson Laboratory, Nucleon Resonances, Sigma-Hyperon photoproduction, vector-meson photoproduction / Includes bibliographical references. / Volker Crede, Professor Directing Dissertation; Anke Meyer-Baese, University Representative; Jorge Piekarewicz, Committee Member; Paul Eugenio, Committee Member; Todd Adams, Committee Member.

In this dissertation, we investigate the approach of pure SU(2) lattice gauge theory to its continuum limit using the deconfinement temperature, six gradient scales, and six cooling scales. We find that cooling scales exhibit similarly good scaling behavior as gradient scales, while being computationally more efficient. In addition, we estimate systematic error in continuum limit extrapolations of scale ratios by comparing standard scaling to asymptotic scaling. Finally we study topological observables in pure SU(2) using cooling to smooth the gauge fields, and investigate the sensitivity of cooling scales to topological charge. We find that large numbers of cooling sweeps lead to metastable charge sectors, without destroying physical instantons, provided the lattice spacing is fine enough and the volume is large enough. Continuum limit estimates of the topological susceptibility are obtained, of which we favor χ 1/4 /T c = 0.643(12). Differences between cooling scales in different topological sectors turn out to be too small to be detectable within our statistical error. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2018. / September 14, 2018. / continuum limit, finite size scaling, lattice field theory, scale, topology / Includes bibliographical references. / Bernd Berg, Professor Co-Directing Dissertation; Laura Reina, Professor Co-Directing Dissertation; Thomas Albrecht-Schmitt, University Representative; Rachel Yohay, Committee Member; Peter Hoeflich, Committee Member.

In this dissertation, Spin-Fermion (SF) models for diluted magnetic semiconductors and high temperature superconducting cuprates are constructed and studied with unbiased numerical techniques. A microscopic model to describe magnetically doped III-V semiconductors is proposed. This model includes the appropriate lattice geometry, as well as, magnetic, spin-orbit, and Coulomb interactions and contains no free parameters. Its study using state-of-the-art numerical techniques provides results in excellent agreement with experimental data for Mn doped GaAs. For the first time, Curie-Weiss behavior of the magnetization is obtained numerically and the values of the Curie temperature are reproduced in a wide range of Mn doping and compensations. We observed that for x (> or = to )3%, the holes are doped into the valence band and uniformly distributed in the material. This could support the "valence band" scenario regarding this material. Phononic degrees of freedom, which are often neglected in studies of high T or = to )3%, the holes are doped into the valence band and uniformly distributed in the material. This could support the "valence band" scenario regarding this material. Phononic degrees of freedom, which are often neglected in studies of high Tc cuprates, are considered in a numerical study of a spin-fermion model. Both diagonal and off-diagonal electron-phonon interactions are considered. While diagonal terms tend to stabilize ordered structures such as stripes, the off-diagonal terms introduce disorder making this structures more dynamical. Our results indicate that phonons play a role in the stabilization of stripe-like states. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2007. / Date of Defense: May 30, 2007. / Spin-Fermion Models, Realistic Lattice Model, High Temperature Cuprates, Multi Band Model, Diluted Magnetic Semiconductors (DMS), Electron-phonon Interactions / Includes bibliographical references. / Nicholas E. Bonesteel, Professor Directing Dissertation; Naresh Dalal, Outside Committee Member; Oskar Vafek, Committee Member; Jorge Piekarewicz, Committee Member; Peng Xiong, Committee Member.

A promising proposal for quantum computation, due to Loss and DiVincenzo, is based on using electron spins in quantum dots as qubits - two-level systems which are the quantum analogues of classical bits. Two-qubit operations (quantum gates) are then carried out by switching on and off the exchange interaction between neighboring spins (i.e. "pulsing" the interaction). This thesis presents a study of the effect of anisotropic corrections to the exchange interaction due to spin-orbit coupling on this scheme. It is shown that time-symmetric pulsing automatically eliminates some undesirable terms in the resulting quantum gates, and well-chosen pulse shapes can produce an effectively isotropic exchange gate which can be used for universal quantum computation. Deviations from perfect time-symmetric pulsing are then studied in the context of a microscopic model of GaAs quantum dots. A new proposal for universal quantum computation which uses control of anisotropic corrections is then presented. In this proposal, the number of pulses required to carry out quantum gates scales as the inverse of a dimensionless measure of the degree of control. The size of this dimensionless figure-of-merit" depends on (i) variation of anisotropy with interdot distance, and (ii) restrictions on the pulse duration due to decoherence for slow pulses and nonadiabatic transitions for fast pulses. Taking these constraints into account, the figure-of-merit is estimated for GaAs quantum dots and shown to be large enough to be useful forquantum computation. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2005. / Date of Defense: June 10, 2005. / Spin-orbit coupling, Quantum dots, Quantum computing / Includes bibliographical references. / Nicholas E. Bonesteel, Professor Directing Thesis; Washington Mio, Outside Committee Member; Vladimir Dobrosavljevi´c, Committee Member; Stephan von Molnar, Committee Member; Mark Riley, Committee Member.

Several models for materials of much current interest in condensed matter physics have been numerically studied, using unbiased methods, including Monte Carlo simulations and exact treatment of the fermionic trace at finite temperature. It was found that many of these materials share common phenomenological aspects due to the presence of intrinsic inhomogeneities in the form of "clustered states". Some of these states are highly susceptible to external perturbations. The list includes diluted magnetic semiconductors and high temperature superconducting cuprates among others. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2004. / Date of Defense: May 12, 2004. / Superconductors, magnetic semiconductors / Includes bibliographical references. / Elbio Dagotto, Professor Directing Dissertation; Naresh Dalal, Outside Committee Member; Adriana Moreo, Committee Member; James Brooks, Committee Member; Jorge Piekarewicz, Committee Member.

Supersymmetric grand unified models based on the SO(10) gauge group are especially attractive in light of recent data on neutrino masses. The simplest SO(10) SUSY GUT models predict unification of third generation Yukawa couplings (t –b – Ƭ) in addition to the usual gauge coupling unification. An assessment of the viability of such Yukawa unified models is presented. For the superpotential Higgs mass parameter μ>0, it is found that unification to less than 1% is possible, but only for GUT scale scalar mass parameter m16 ~ 8 – 20 TeV, and small values of gaugino mass m1/2 ≤ 150 GeV. Such models require tha a GUT scale mass splitting exists amongst Higgs scalars with m2Hu < m2Hd. Viable solutions lead to a radiatively generated inverted scalar mass hierarchy, with third generation and Higgs scalars being lighter than other sfermions. These models have a very heavy sfermions, so that unwanted flavor changing and CP violating SUSY processes are suppressed, but may suffer from some fine-tuning requirements. While the generated spectra satisify b → sγ and (g – 2)μ constraints, there exists tension with the dark matter relic density unless m16 ≤ 3TeV. These models offer prospects for SUSY discovery at the Fermilab Tevatron collider via the search for W1Z2 → 3l events, or via gluino pair production. If μ < 0, Yujawa coupling unification to less than 5% can occur for m16 and m 1/2≥ 1 – 2 TeV. Consistency of negative μ Yukawa unified models with b → sγ, (g – 2)μ, and relic density Ωh2 all imply very large values of m1/2 typically greater than about 2.5 TeV, in which case direct dection of sparticles may be a challenge even at the LHC. To address the tension between Yukawa unification and the excess of dark matter that the μ>0 models tend to predict, a couple of possible improvements are surveyed. One solution- lowering the GUT scale mass value of first and second generation scalars, leads to uR and cR squark masses in the 90 – 120 GeV regime, which should be accessible to Fermilab Tavatron experiments. Another possibility is relaxing gaugino mass universality which may solve the relic density problem by having neutralino annihilations via the Z or h resonances, or by having a wino-like LSP. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2004. / Date of Defense: August 31, 2004. / SUSY, GUT, Supersymmetry Phenomenology, Supersymmetric Standard Model, Yukawa Unification, SO(10) Symmetry / Includes bibliographical references. / Howard Baer, Professor Directing Dissertation; Christopher Hunter, Outside Committee Member; Laura Reina, Committee Member; Harrison Prosper, Committee Member; Jorge Piekarewicz, Committee Member.