# Alumni Dissertations

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### Magnetic deflagration in the molecular magnet Mn12-ac

Author:Sean McHughYear of Dissertation:2009Program:PhysicsAdvisor:Myriam SarachikAbstract:In 1995, Paulsen and Park observed abrupt spontaneous reversals of the magnetization in crystals of the molecular magnet Mn12-ac, which they dubbed ``magnetic avalanches". They suggested that the magnetic avalanches were a thermal runaway process where the reversing spins release heat stimulating further relaxation. Various exotic phenomena were proposed as an alternative explanations. In 2005, Suzuki et al. established that this spontaneous magnetic relaxation occurs as a ``front" separating regions of opposing magnetization that propagates at a constant speed through the crystal. They suggested that this propagating front is analogous to a flame in chemical deflagration and introduced the thermal relaxation process, magnetic deflagration. The analysis presented there was limited by lack of data. A more thorough comparison with the theory would require the ability to trigger avalanches in a more controlled way rather than wait for their spontaneous occurrence. The work presented in this thesis is a continuation of the program initiated by Suzuki. Significant progress experimental progress has been made allowing us to trigger avalanches over a wide range of conditions. The magnetization dynamics and the ignition temperatures are studied in detail using an array of micro-sized Hall sensors and Germanium thermometers. In addition, we report the existence of a new species of avalanches consisting only of the fast-relaxing isomers of Mn12-ac, the so-called ``minor species". We explore avalanches of both species, as well as the interaction between them. Finally, a detailed analysis is performed to compare the experiment with the theory of magnetic deflagration. We find the theory of magnetic deflagration to be consistent with the data and extract values for the key physical quantities: the thermal diffusivity and avalanche front temperatures. Agreement between our predicted values and an independent measurement of these quantities would provide compelling verification of the theory.

### Solid State NMR Studies of Materials for Energy Technology

Author:Chandana Nambukara Kodiweera ArachchilageYear of Dissertation:2010Program:PhysicsAdvisor:Steve GreenbaumAbstract:Abstract SOLID STATE NMR STUDIES OF MATERIALS FOR ENERGY TECHNOLOGY by Chandana K. Nambukara Kodiweera Arachchilage Adviser: Professor Steve Greenbaum Presented in this thesis are NMR investigations of the dynamical and structural properties of materials for energy conversion and storage devices. 1H and 2H NMR was used to study water and methanol transportation in sulfonated poly(arylene ether ketone) based membranes for direct methanol fuel cells (DMFC). These results are presented in chapter 3. The amount of liquid in the membrane and ion exchange capacity (IEC) are two main factors that govern the dynamics in these membranes. Water and methanol diffusion coefficients also are comparable. Chapters 4 and 5 are concerned with 31P and 1H NMR in phosphoric acid doped PBI membranes (para-PBI and 2OH-PBI) as well as PBI membranes containing ionic liquids (H3PO4/PMIH2PO4/PBI). These membranes are designed for higher-temperature fuel cell operation. In general, stronger short and long range interactions were observed in the 2OH-PBI matrix, yielding reduced proton transport compared to that of para-PBI. In the case of H3PO4/PMIH2PO4/PBI, both conductivity and diffusion are higher for the sample with molar ratio 2/4/1. Finally, chapter 6 is devoted to the 31P NMR MAS study of phosphorus-containing structural groups on the surfaces of micro/mesoporous activated carbons. Two spectral features were observed and the narrow feature identifies surface phosphates while the broad component identifies heterogeneous subsurface phosphorus environments including phosphate and more complex structure multiple P-C, P-N and P=N bonds.

### Solid State NMR Studies of Materials for Energy Technology

Author:Chandana Nambukara Kodiweera ArachchilageYear of Dissertation:2010Program:PhysicsAdvisor:Steve GreenbaumAbstract:Abstract SOLID STATE NMR STUDIES OF MATERIALS FOR ENERGY TECHNOLOGY by Chandana K. Nambukara Kodiweera Arachchilage Adviser: Professor Steve Greenbaum Presented in this thesis are NMR investigations of the dynamical and structural properties of materials for energy conversion and storage devices. 1H and 2H NMR was used to study water and methanol transportation in sulfonated poly(arylene ether ketone) based membranes for direct methanol fuel cells (DMFC). These results are presented in chapter 3. The amount of liquid in the membrane and ion exchange capacity (IEC) are two main factors that govern the dynamics in these membranes. Water and methanol diffusion coefficients also are comparable. Chapters 4 and 5 are concerned with 31P and 1H NMR in phosphoric acid doped PBI membranes (para-PBI and 2OH-PBI) as well as PBI membranes containing ionic liquids (H3PO4/PMIH2PO4/PBI). These membranes are designed for higher-temperature fuel cell operation. In general, stronger short and long range interactions were observed in the 2OH-PBI matrix, yielding reduced proton transport compared to that of para-PBI. In the case of H3PO4/PMIH2PO4/PBI, both conductivity and diffusion are higher for the sample with molar ratio 2/4/1. Finally, chapter 6 is devoted to the 31P NMR MAS study of phosphorus-containing structural groups on the surfaces of micro/mesoporous activated carbons. Two spectral features were observed and the narrow feature identifies surface phosphates while the broad component identifies heterogeneous subsurface phosphorus environments including phosphate and more complex structure multiple P-C, P-N and P=N bonds.

### Nuclear Magnetic Resonance Studies on Lithium and Sodium Electrode Materials for Rechargeable Batteries

Author:Tetiana NosachYear of Dissertation:2014Program:PhysicsAdvisor:Steve GreenbaumAbstract:In this thesis, Nuclear Magnetic Resonance (NMR) spectroscopic techniques are used to study lithium and sodium electrode materials for advanced rechargeable batteries. Three projects are described in this thesis. The first two projects involve 6Li, 7Li and 31P NMR studies of two cathode materials for advanced rechargeable batteries. The third project is a study of sodium titanate cathode materials for Na-ion batteries, where 1H, 7Li, and 23Na static and magic angle spinning NMR were used in order to obtain detailed information on the chemical environments.

### Quantum Rotational Effects in Nanomagnetic Systems

Author:Michael O'KeeffeYear of Dissertation:2013Program:PhysicsAdvisor:Eugene ChudnovskyAbstract:Quantum tunneling of the magnetic moment in a nanomagnet must conserve the total angular momentum. For a nanomagnet embedded in a rigid body, reversal of the magnetic moment will cause the body to rotate as a whole. When embedded in an elastic environment, tunneling of the magnetic moment will cause local elastic twists of the crystal structure. In this thesis, I will present a theoretical study of the interplay between magnetization and rotations in a variety of nanomagnetic systems which have some degree of rotational freedom. We investigate the effect of rotational freedom on the tunnel splitting of a nanomagnet which is free to rotate about its easy axis. Calculating the exact instanton of the coupled equations of motion shows that mechanical freedom of the particle renormalizes the easy axis anisotropy, increasing the tunnel splitting. To understand magnetization dynamics in free particles, we study a quantum mechanical model of a tunneling spin embedded in a rigid rotor. The exact energy levels for a symmetric rotor exhibit first and second order quantum phase transitions between states with different values the magnetic moment. A quantum phase diagram is obtained in which the magnetic moment depends strongly on the moments of inertia. An intrinsic contribution to decoherence of current oscillations of a flux qubit must come from the angular momentum it transfers to the surrounding body. Within exactly solvable models of a qubit embedded in a rigid body and an elastic medium, we show that slow decoherence is permitted if the solid is macroscopically large. The spin-boson model is one of the simplest representations of a two-level system interacting with a quantum harmonic oscillator, yet has eluded a closed-form solution. I investigate some possible approaches to understanding its spectrum. The Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator show that for certain parameter ranges the system exhibits multiple Landau-Zener transitions. These transitions coincide in time with changes in the oscillator dynamics. A large number of spins on a single oscillator coupled only through the in-phase oscillations behaves as a single large spin, greatly enhancing the spin-phonon coupling.

### Strategies for Discriminating and Comparing Unknown Unitary Transformations

Author:Guy OkokoYear of Dissertation:2014Program:PhysicsAdvisor:Janos BergouAbstract:How to discriminate or compare two unitary transformations that are completely unknown? We first examine the unambiguous discrimination of two unknown unitary transformations; we show that the results are the same as those found for the programmable discrimination of two unknown quantum states. Next we consider the minimum-error comparison of two unknown unitary transformations; the results are obtained in the general case where the prior probabilities are different. Last we study the unambiguous discrimination of two unknown unitary transformations in the case where multiple copies of data are available.

### Colloidal Quantum Dot Based Photonic Circuits and Devices

Author:Nicky OkoyeYear of Dissertation:2014Program:PhysicsAdvisor:Vinod MenonAbstract:Colloidal quantum dots have desirable optical properties which can be exploited to realize a variety of photonic devices and functionalities. However, colloidal dots have not had a pervasive utility in photonic devices because of the absence of patterning methods. The electronic chip industry is highly successful due to the well-established lithographic procedures. In this thesis we borrow ideas from the semiconductor industry to develop lithographic techniques that can be used to pattern colloidal quantum dots while ensuring that the optical properties of the quantum dots are not affected by the process. In this thesis we have developed colloidal quantum dot based waveguide structures for amplification and switching applications for all-optical signal processing. We have also developed colloidal quantum dot based light emitting diodes. We successfully introduced CdSe/ZnS quantum dots into a UV curable photo-resist, which was then patterned to realize active devices. In addition, "passive" devices (devices without quantum dots) were integrated to "active" devices via waveguide couplers. Use of photo-resist devices offers two distinct advantages. First, they have low scattering loss and secondly, they allow good fiber to waveguide coupling efficiency due to the low refractive index which allows for large waveguide cross-sections while supporting single mode operation. Practical planar photonic devices and circuits incorporating both active and passive structures can now be realized, now that we have patterning capabilities of quantum dots while maintaining the original optical attributes of the system. In addition to the photo-resist host, we also explored the incorporation of colloidal quantum dots into a dielectric silicon dioxide and silicon nitride one-dimensional microcavity structures using low temperature plasma enhanced chemical vapor deposition. This material system can be used to realize microcavity light emitting diodes that can be realized on any substrate. As a proof of concept demonstration we show a 1550 nm emitting all-dielectric vertical cavity structure embedded with PbS quantum dots. Enhancement in spontaneous emission from the dots embedded in the microcavity is also demonstrated.

### Wave Scattering in Random Layered Media

Author:Jongchul ParkYear of Dissertation:2010Program:PhysicsAdvisor:Azriel GenackAbstract:The scaling and statistics of the transport of waves in random media depend strongly on the dimensionality of the medium. The statistic of transmission in one dimension (1D) and quasi-1D (Q1D) have been calculated and tested. However, the statistic for other dimensions has not been established. Exploring transport in a layered system of stacks of glass cover slips with transverse nonuniformity has allowed us to study a dimensional crossover in transport from 1D towards 3D. The crossover occurs when the lateral spread of the wave become larger than the transverse coherence length in the transmitted speckle pattern as the number of layers increases. In thin samples, in which light does not spread beyond a single coherence area of the field on the output surface, the statistics of normalized intensity follow 1D statistics associated with a segment of a log-normal distribution with a sharp drop below the log-normal distribution for low values of intensity. Once the lateral spread is larger than the transverse coherence length, the probability density of intensity becomes a mixture of a mesoscopic distribution and an intensity distribution of a Gaussian field. This distribution was originally found for Q1D. Beyond 1D, the intensity statistics have a same form as Q1D statistics which is a function of a single localization parameter, the “statistical conductance”

g ’. This transition from 1D to Q1D statistics reflects a topological change in the transmitted field. In 1D, the transmitted intensity never vanishes, while beyond 1D, a speckle pattern built upon a network of phase singularities forms.### Initial conditions in high-energy collisions

Author:Elena PetreskaYear of Dissertation:2014Program:PhysicsAdvisor:Adrian DumitruAbstract: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.

### PHASE SPACE EXPLORATIONS IN TIME DEPENDENT DENSITY FUNCTIONAL THEORY

Author:ARUNA RAJAMYear of Dissertation:2010Program:PhysicsAdvisor:Neepa MaitraAbstract: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.