# Alumni Dissertations and Theses

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### Nanoacoustic Effects in Type-II Superconductors and Decoherence of Two-state Systems

Author:Jaroslav AlbertYear of Dissertation:2009Program:PhysicsAdvisor:Eugene ChudnovskyAbstract:In this thesis we focus on two areas of research: nanoacoustic effects in superconductors, and decoherence of two-state systems due to radiation of acoustic phonons. In the first part of this thesis we propose two new nanoacoustic effects: induction of voltage by mechanical stress, and nucleation of a superconducting vortex by an acoustic standing wave. Both of these effects take place in type-II superconductors. In the second part we study relaxation processes via acoustic phonons of a particle in a double-well potential and of a flux qubit. Part 1: Mechanical stress causes motion of dislocations in solids. In a type-II superconductor a moving dislocation generates a pattern of current that exerts a force on the surrounding vortex lattice capable of depinning it. We show that the concentration and the speed of dislocations needed to produce depinning currents are within practical range. When external magnetic field and transport current are present, this effect generates voltage across the superconductor. In this manner, a type-II superconductor can serve as an electrical sensor of the mechanical stress. Nucleation of vortices in a superconductor below the first critical field can be assisted by transverse sound in the GHz frequency range. We work out from energy considerations that, in the presence of a sound wave, vortices enter and exit the superconductor at the frequency of the sound. The computed threshold parameters of the sound are shown to be within experimental reach. Part 2: We propose a method of computing phonon-induced relaxation of two-state systems that is based on symmetry arguments. This allows one to express the rates in terms of independently measurable parameters. For translationally and rotationally invariant systems the conservation of linear and angular momenta must be taken into account when formulating the interaction Hamiltonian. For a particle (e.g., electron or proton) in a rigid double-well potential embedded in a solid the rate is proportional to the seventh power of temperature. For a flux qubit the two-phonon relaxation is important only if the size of the qubit is much smaller than the phonon wavelength. Due to symmetry the two-phonon rate of both systems is proportional to the square of the bias. This allows for additional control of the relaxation rate.

### Nanoacoustic Effects in Type-II Superconductors and Decoherence of Two-state Systems

Author:Jaroslav AlbertYear of Dissertation:2009Program:PhysicsAdvisor:Eugene ChudnovskyAbstract:In this thesis we focus on two areas of research: nanoacoustic effects in superconductors, and decoherence of two-state systems due to radiation of acoustic phonons. In the first part of this thesis we propose two new nanoacoustic effects: induction of voltage by mechanical stress, and nucleation of a superconducting vortex by an acoustic standing wave. Both of these effects take place in type-II superconductors. In the second part we study relaxation processes via acoustic phonons of a particle in a double-well potential and of a flux qubit. Part 1: Mechanical stress causes motion of dislocations in solids. In a type-II superconductor a moving dislocation generates a pattern of current that exerts a force on the surrounding vortex lattice capable of depinning it. We show that the concentration and the speed of dislocations needed to produce depinning currents are within practical range. When external magnetic field and transport current are present, this effect generates voltage across the superconductor. In this manner, a type-II superconductor can serve as an electrical sensor of the mechanical stress. Nucleation of vortices in a superconductor below the first critical field can be assisted by transverse sound in the GHz frequency range. We work out from energy considerations that, in the presence of a sound wave, vortices enter and exit the superconductor at the frequency of the sound. The computed threshold parameters of the sound are shown to be within experimental reach. Part 2: We propose a method of computing phonon-induced relaxation of two-state systems that is based on symmetry arguments. This allows one to express the rates in terms of independently measurable parameters. For translationally and rotationally invariant systems the conservation of linear and angular momenta must be taken into account when formulating the interaction Hamiltonian. For a particle (e.g., electron or proton) in a rigid double-well potential embedded in a solid the rate is proportional to the seventh power of temperature. For a flux qubit the two-phonon relaxation is important only if the size of the qubit is much smaller than the phonon wavelength. Due to symmetry the two-phonon rate of both systems is proportional to the square of the bias. This allows for additional control of the relaxation rate.

### Quantum dislocations in solid Helium-4

Author:Darya AleinikavaYear of Dissertation:2012Program:PhysicsAdvisor:Anatoly KuklovAbstract:In this thesis the following problems on properties of solid

4 He are considered: i) the role of long-range interactions in suppression of dislocation roughening at T = 0; ii) the combined effect of3 He impurities and Peierls potential on shear modulus softening; iii) the dislocation superclimb and its connection to the phenomenon of “giant isochoric compressibility” ; iv) non-linear dislocation response to the applied stress and stress-induces dislocation roughening as a I-order phase transition in 1D at finite temperature. First we investigate the effect of long-range interactions on the state of edge dislocation at T = 0. Such interactions are induced by elastic forces of the solid. We found that quantum roughening transition of a dislocation at T = 0 is completely suppressed by arbitrarily small long-range interactions between kinks. A heuristic argument is presented and the result has been verified by numerical Monte-Carlo simulations using Worm Algorithm in J-current model. It was shown that the Peierls potential plays a crucial role in explaining the elastic properties of dislocations, namely shear modulus softening phenomenon. The crossover from T = 0 to finite temperatures leads to intrinsic softening of the shear modulus and issolely controlled by kink typical energy. It was demonstrated that the mechanism, involving only the binding of3 He impurities to the dislocations, requires an unrealistically high concentrations of defects (or impurities) in order to explain the shear modulus phenomenon and therefore an inclusion of Peierls potential in consideration is required. Superclimbing dislocations, that is the edge dislocations with the superfluidity along the core, were investigated. The theoretical prediction that superclimb is responsible for the phenomenon of “giant isochoric compressibility ” was confirmed by Monte-Carlo simulations. It was demonstrated that the isochoric compressibility is suppressed at low temperatures. The dependence of compressibility on the dislocation length was shown to be strongly dependent on long-range interaction. Non-linear behavior at high stresses was considered. The dislocation was observed to exhibit two types of behavior depending on the dislocation size: reversible and hysteretic. In the reversible regime responses of superclimbing dislocations exhibit sharp resonant peaks. We attribute this feature to the resonant creation of jog-antijog pairs. The peak in the compressibility results in the dip in the speed of sound which we believe was observed in “ UMASS-sandwich” mass-transport experiments. The hysteresis revealed an unusually strong sensitivity to the dislocation size signifying that the stress-induced roughening is a I-order phase transition in 1D at finite T.### COMPUTATIONAL INSIGHTS INTO THE OXYGEN EVOLVING COMPLEX OF PHOTOSYSTEM ΙΙ

Author:Muhamed AminYear of Dissertation:2014Program:PhysicsAdvisor:Marilyn GunnerAbstract:The Oxygen Evolving Complex (OEC) of Photosystem II (PSII) is a unique Mn4O5Ca2+ cluster that catalyzes the photoactivated water splitting reaction. The OEC is a model system for bio-inspired artificial systems to use solar energy to pull electrons from water to produce fuel. The OEC goes through a cycle of 5 S states storing 4 holes, via electron transfer to P680+, the primary electron donor in PSII to generate a high valence S4 state that oxidizes water. The key questions are what controls the order of oxidation and deprotonation of the OEC complex and how does the PSII protein modulate the cluster behavior. Here, we present a classical electrostatics Monte Carlo (MC) technique, with input from density functional theory (DFT) and molecular dynamics (MD) to study the thermodynamics of the S0 to S3 states in a cluster embedded in the whole PSII. The model is tested against model complexes and yields a very good agreement with the experiment. In the simulation, the electrochemical potential (Eh) is varied to oxidize the OEC. The MC sampling allows the Âµ-oxo-bridges, terminal waters and amino acid residues to change their protonation states and/or their rotamer position to respond to the Mn oxidation. In addition, chloride is allowed to move during the cycle. The order of Mn oxidation found here is Mn2, Mn3, Mn4 and finally Mn1 as the system goes from the S0 to S3 states. In the S-1 state O1 and O4 are protonated as are the terminal waters on Mn4 and the Ca2+. O4 and O1 are deprotonated when S0 and S1 are formed respectively. The formation of S2 includes proton transfer from W2 to the nearby D61, reducing the release of protons to the media, consistent with experimental measurements. Protons are also lost from H337 and E329. The proton-release pattern is compared fixing the protonation states for H337, D61, terminal waters and with chloride-depleted PSII. The calculated midpoint potential of each Mn and their dependence on pH is discussed.

### Electrodynamics of Nearly Ferroelectric Superconductors in the local London and non-local Pippard limits

Author:Upali AparajitaYear of Dissertation:2010Program:PhysicsAdvisor:Joseph BirmanAbstract:In this work, electrodynamics of a Nearly Ferroelectric Superconduct- ing (NFE-SC) material in local London limit and nonlocal Pippard limit is reported. NFE-SC materials exhibit superconductivity and are in a nearly- ferroelectric state. One example of such materials is 'n' or 'p' doped $SrTiO_3$ . The structure of a single vortex in an NFE-SC thin film is explored. Taking $n-SrTiO_3$ as our sample of choice, the frequency dependent magnetic field and current within the sample are calculated. The expulsion of the vortex from the sample at resonances is observed. The interaction between two vortices due to the presence of high background dielectric is explored. The effect of finite thickness on the vortex structure is explored for an NFE-SC film. With increase in film thickness, the resonances become sharper and as a result the system undergoes oscillatory transition between ferroelectric, superconducting and Meissner-like states. Nonlocal effects in the NFE-SC thin film are explored in the Pippard limit. Specular Reflection and Random scattering are studied. Analytical as well as numerical methods are used to investigate the nature of the material and solve for the current and magnetic field within the sample. The current is found to be non-zero within the sample. The material properties can be manipulated to enhance or expel the current from within the sample with the change in frequency. The material shows complex transitions between Type-I, Type-II superconducting as well as Dielectric states. Numerical codes developed for the solution of the integro-differential equations are given.

### Electrodynamics of Nearly Ferroelectric Superconductors in the local London and non-local Pippard limits

Author:Upali AparajitaYear of Dissertation:2010Program:PhysicsAdvisor:Joseph BirmanAbstract:In this work, electrodynamics of a Nearly Ferroelectric Superconduct- ing (NFE-SC) material in local London limit and nonlocal Pippard limit is reported. NFE-SC materials exhibit superconductivity and are in a nearly- ferroelectric state. One example of such materials is 'n' or 'p' doped $SrTiO_3$ . The structure of a single vortex in an NFE-SC thin film is explored. Taking $n-SrTiO_3$ as our sample of choice, the frequency dependent magnetic field and current within the sample are calculated. The expulsion of the vortex from the sample at resonances is observed. The interaction between two vortices due to the presence of high background dielectric is explored. The effect of finite thickness on the vortex structure is explored for an NFE-SC film. With increase in film thickness, the resonances become sharper and as a result the system undergoes oscillatory transition between ferroelectric, superconducting and Meissner-like states. Nonlocal effects in the NFE-SC thin film are explored in the Pippard limit. Specular Reflection and Random scattering are studied. Analytical as well as numerical methods are used to investigate the nature of the material and solve for the current and magnetic field within the sample. The current is found to be non-zero within the sample. The material properties can be manipulated to enhance or expel the current from within the sample with the change in frequency. The material shows complex transitions between Type-I, Type-II superconducting as well as Dielectric states. Numerical codes developed for the solution of the integro-differential equations are given.

### Solid State Nuclear Magnetic Resonance Investigations of Advanced Energy Materials

Author:George BennettYear of Dissertation:2009Program:PhysicsAdvisor:Steve GreenbaumAbstract:In order to better understand the physical electrochemical changes that take place in lithium ion batteries and asymmetric hybrid supercapacitors solid state nuclear magnetic resonance (NMR) spectroscopy has been useful to probe and identify changes on the atomic and molecular level. NMR is used to characterize the local environment and investigate the dynamical properties of materials used in electrochemical storage devices (ESD). NMR investigations was used to better understand the chemical composition of the solid electrolyte interphase which form on the negative and positive electrodes of lithium batteries as well as identify the breakdown products that occur in the operation of the asymmetric hybrid supercapacitors. The use of nano-structured particles in the development of new materials causes changes in the electrical, structural and other material properties. NMR was used to investigate the affects of fluorinated and non fluorinated single wall nanotubes (SWNT). In this thesis three experiments were performed using solid state NMR samples to better characterize them. The electrochemical reactions of a lithium ion battery determine its operational profile. Numerous means have been employed to enhance battery cycle life and operating temperature range. One primary means is the choice and makeup of the electrolyte. This study focuses on the characteristics of the solid electrolyte interphase (SEI) that is formed on the electrodes surface during the charge discharge cycle. The electrolyte in this study was altered with several additives in order to determine the influence of the additives on SEI formation as well as the intercalation and de-intercalation of lithium ions in the electrodes. 7Li NMR studies where used to characterize the SEI and its composition. Solid state NMR studies of the carbon enriched acetonitrile electrolyte in a nonaqueous asymmetric hybrid supercapacitor were performed. Magic angle spinning (MAS) coupled with cross polarization NMR techniques were used to determine what effects 200 ppm of intentionally added water would have on the decomposition of the acetonitrile. The resultant NMR spectra yielded several prominent peaks which were assigned to acetamide, glycolonitrile, formaldehyde and other lithium carbon derivatives. The aforementioned decomposition products are a believed to be a result of the acetonitrile being hydrolyzed as well as its interaction with the lithium salt. The decomposition products are deposited on electrode surface leading to operation changes in the life of the supercapacitors. The information gained from the NMR studies may be beneficial understanding the supercapacitor operation and aid in future design. Carbon nanotubes are used to enhance structural stability and performance. In this experiment NMR is used to determine if the addition of nanotubes to two types of polymer matrix changes the structural stiffness and motional dynamics. The polymers studied by direct 1H NMR observations are Polybutadiene (PB) and Polyisobutylene (PIB). PB and PIB with single walled carbon nanotubes (SWNT) as well as functionalized with fluorine (F) produce significantly stronger composites as compared to composites without SWNT.

### MESSAGE PASSING TECHNIQUES FOR STATISTICAL PHYSICS AND OPTIMIZATION IN COMPLEX SYSTEMS

Author:Lin BoYear of Dissertation:2014Program:PhysicsAdvisor:Hernan MakseAbstract:Optimization problem has always been considered as a central topic in various areas of science and engineering. It aims at finding the configuration of a large number of variables with which the objective function is optimal. The close relation between optimization problems and statistical physics through the probability measure of the Boltzmann type has brought new theoretical tools from statistical physics of disordered systems to optimization problems. In this thesis, we use message passing techniques, in particular cavity method, developed in the last decades within spin glass theory to study optimization problems in complex systems. In the study of force transmission in jammed disordered systems, we develop a mean-field theory based on the consideration of the contact network as a random graph where the force transmission becomes a constraint satisfaction problem, with which the constraints enforce force and torque balances on each particle. We thus use cavity method to compute the force distribution for random packings of hard particles of any shape, with or without friction and find a new signature of jamming in the small force behavior whose exponent has attracted recent active interest. Furthermore, we relate the force distribution to a lower bound of the average coordination number of jammed packings of frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings. Another application of the cavity method is immunization strategies. We study the problem of finding the most influential set of nodes in interaction networks to immunize against epidemics. By means of cavity method approach, we propose a new immunization strategy to identify immunization targets efficiently with respect to the susceptable-infected-recovered epidemic model. We implement our method on computer-generated random graphs and real networks and find that our new immunization strategy can significantly reduce the size of epidemic.

### Entropy of Jammed Granular Matter

Author:Christopher BriscoeYear of Dissertation:2009Program:PhysicsAdvisor:Hernan MakseAbstract:Granular matter can be considered a non-equilibrium system, such that equilibrium statistics is insufficient to describe the dynamics. A phase transition occurs when granular materials are compressed such that a nonzero stress develops in response to a strain deformation. This transition, referred to as the jamming transition, occurs at a critical volume fraction, depending on friction and preparation protocol. Analysis of the jamming transition produces a phase diagram of jammed granular matter for identical spheres, characterized by the critical volume fraction, and the average coordination number. The boundaries of the phase diagram are related to well-defined upper and lower limits in the density of disordered packings; random close packing (RCP) and random loose packing (RLP). Frictional systems, such as granular matter, exhibit an inherent path dependency resulting in the loss of energy conservation, an important facet of equilibrium statistics. It has been suggested Edwards that the volume-force (V-F) ensemble, wherein volume replaces energy as the conservative quantity, may provide a sufficient framework to create a statistical ensemble for jammed granular matter. Treating a jammed system via the V-F ensemble introduces an analogue to temperature in equilibrium systems. This analogue, "compactivity", measures how compact a system could be and governs fluctuation in the volume statistics. Randomness in statistical systems is typically characterized by entropy, the equation of state derived from the number of microstates available to the system. In equilibrium statistical mechanics, entropy provides the link between these microstates and the macroscopic thermodynamic properties of the system. Therefore, calculating the entropy within the V-F ensemble can relate the available microscopic volume for each grain to the macroscopic system properties. The entropy is shown to be minimal at RCP and maximal at the minimum RLP limit, via several methods utilizing simulations and theoretical models. Within this framework RCP is achieved in the limit of minimal compactivity and RLP is achieved in the limit of maximal compactivity. The boundaries of a phase diagram for jammed matter could thereby be defined by the limits of zero and infinite compactivities, characterizing the RCP and RLP limits of granular matter.

### Entropy of Jammed Granular Matter

Author:Christopher BriscoeYear of Dissertation:2009Program:PhysicsAdvisor:Hernan MakseAbstract:Granular matter can be considered a non-equilibrium system, such that equilibrium statistics is insufficient to describe the dynamics. A phase transition occurs when granular materials are compressed such that a nonzero stress develops in response to a strain deformation. This transition, referred to as the jamming transition, occurs at a critical volume fraction, depending on friction and preparation protocol. Analysis of the jamming transition produces a phase diagram of jammed granular matter for identical spheres, characterized by the critical volume fraction, and the average coordination number. The boundaries of the phase diagram are related to well-defined upper and lower limits in the density of disordered packings; random close packing (RCP) and random loose packing (RLP). Frictional systems, such as granular matter, exhibit an inherent path dependency resulting in the loss of energy conservation, an important facet of equilibrium statistics. It has been suggested Edwards that the volume-force (V-F) ensemble, wherein volume replaces energy as the conservative quantity, may provide a sufficient framework to create a statistical ensemble for jammed granular matter. Treating a jammed system via the V-F ensemble introduces an analogue to temperature in equilibrium systems. This analogue, "compactivity", measures how compact a system could be and governs fluctuation in the volume statistics. Randomness in statistical systems is typically characterized by entropy, the equation of state derived from the number of microstates available to the system. In equilibrium statistical mechanics, entropy provides the link between these microstates and the macroscopic thermodynamic properties of the system. Therefore, calculating the entropy within the V-F ensemble can relate the available microscopic volume for each grain to the macroscopic system properties. The entropy is shown to be minimal at RCP and maximal at the minimum RLP limit, via several methods utilizing simulations and theoretical models. Within this framework RCP is achieved in the limit of minimal compactivity and RLP is achieved in the limit of maximal compactivity. The boundaries of a phase diagram for jammed matter could thereby be defined by the limits of zero and infinite compactivities, characterizing the RCP and RLP limits of granular matter.