# Alumni Dissertations

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### POTENTIAL ENERGY LANDSCAPE OF PARTICULATE MATTER

Author:Kun WangYear of Dissertation:2012Program:PhysicsAdvisor:Hernan MakseAbstract:The application of concepts from equilibrium statistical mechanics to out of equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. These systems are considered "complex" since equilibrium statistics is insufficient in its attempt to describe the system dynamics. An appealing approach for understanding these complex systems is to study the properties of the system's "potential energy landscape" (PEL), described by the 3N-coordinates of all particles in the multi-dimensional configuration space, or landscape, of the potential energy of the system (N is the number of particles). For dissipative jammed systems- granular materials or droplets- a key concept introduced by S. Edwards in 1989 is to replace the energy ensemble describing conservative systems by the volume ensemble. However, this approach is no able to describe the jamming critical point (J-point) for deformable particles like emulsions, whose geometric configurations are influenced by the applied external stress. Therefore, the volume ensemble requires augmentation by the ensemble of stresses. Just as volume fluctuations in the Edwards ensemble can be described by compactivity, the stress fluctuations give rise to an angoricity, another analogue of temperature in equilibrium systems. In this Thesis, we test the combined volume-stress ensemble for granular matter by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble as a test of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. These intensive variables elucidate the thermodynamic order of the jamming phase transition by showing the absence of critical fluctuations above jamming in static observables like pressure and volume. Our results demonstrate the possibility of calculating important observables such as the entropy, volume, pressure, coordination number and the distribution of interparticle forces to fully characterize the scaling laws near the jamming transition from a statistical mechanics point of view. We also study the energy-landscape network. We find the stable basins and the first order saddles connecting them, and identify them with the network nodes and links, respectively. We analyze the network properties and model the system's evolution.

### QUASI-NORMAL MODES IN RANDOM MEDIA

Author:Jing WangYear of Dissertation:2012Program:PhysicsAdvisor:Azriel GenackAbstract:This thesis is an experimental study of microwave transmission through quasi-one-dimensional random samples via quasi-normal modes. We have analyzed spectra of localized microwave transmitted through quasi-one-dimensional random samples to obtain the central frequency, linewidth and field speckle pattern of the modes for an ensemble of samples at three lengths. We find strong correlation between modal field speckle patterns. This leads to destructive interference between modes which explain strong suppression of steady state transmission and of pulsed transmission at early times. At longer times, the rate of decay of transmission slows down because of the increasing prominence of long-lived modes. We have also studied the statistics of mode spacings and widths in localized samples. The distribution of mode spacings between adjacent modes is close to the Wigner surmise predicted for diffusive waves, which exhibit strong level repulsion. However, a deviation from Wigner distribution can be seen in the distribution of spacings beyond the nearest ones. A weakening in the rigidity of the modal spectrum is also observed as the sample length increases because of reduced level repulsion for more strongly localized waves. In contrast to residual diffusive behavior for level spacing statistics, the distribution of level widths are log-normal as predicted for localized waves. But the residual diffusive behavior can be seen from the smaller variance of the normalized mode width as compared to predictions for strongly localized waves. We also measured the steady state and dynamic fluctuations and correlation of localized microwave transmitted through random waveguides. We find the degree of intensity correlation first increases, and then decays with time delay, before increasing dramatically. The variation in the spatial correlation of intensity with time delay is due to the changing effective number of modes that contribute to transmission. A minimum in correlation is reached when the number of modes contributing appreciably to transmission peaks. At long times, the degree of intensity correlation and the variance of total transmission increase dramatically. This reflects the reduced role of short-lived overlapping states and the growing weight of long-lived spectrally isolated modes.

### STATISTICAL MECHANICS OF JAMMED MATTER

Author:Ping WangYear of Dissertation:2009Program:PhysicsAdvisor:Hernan MakseAbstract:In a thermal system, the Brownian motion of the constituent particles implies that the system dynamically explores the available energy landscape, such that the notion of a statistical ensemble applies. For densely packed systems of interest in this study, in which enduring contacts between particles are important, the potential energy barrier prohibits an equivalent random motion. At first sight it seems that the thermal statistical mechanics do not apply to these systems as there is no mechanism for averaging over the configurational states. Hence, these systems are inherently out of equilibrium. On the other hand, if the granular material is gently tapped such that the grains can slowly explore the available configurations, the situation becomes analogous to the equilibrium case scenario. It has been shown that the volume of the system is dependent on the applied tapping regime, and that this dependence is reversible, implying ergodicity. This result gives support to the proposed statistical ensemble valid for dense, static and slowly moving granular materials which was first introduced by Edwards and Oakeshott in 1989. Through this approach, notions of macroscopic quantities such as entropy and compactivity were also introduced to granular matter.

### Dipolar interactions, long range order and random fields in a single molecule magnet, Mn12-acetate

Author:Bo WenYear of Dissertation:2013Program:PhysicsAdvisor:Myriam SarachikAbstract:In this thesis, I will present an experimental study of two single molecule magnets, Mn

_{12}–ac and Mn_{12}–ac–MeOH. I will show that in both systems, the temperature dependence of the inverse susceptibility yields a positive intercept on the temperature axis (a positive Weiss temperature), implying the existence of a ferromagnetic phase at low temperature. Applying a magnetic field in the transverse direction moves the Weiss temperature downward towards zero. This implies that the transverse field triggers mechanisms in the system that compete with the dipolar interaction and suppress the long–range ordering. I will then show that the suppression in Mn_{12}–ac is considerably stronger than that expected for a pure TFIFM (Transverse Field Ising Ferromagnetic) model system. By contrast, the behavior of Mn_{12}–ac–MeOH is consistent with the model. We attribute the difference between the two systems to the presence of randomness in Mn_{12}–ac associated with isomer disorder. Thus, in addition to spin–canting and thermal fluctuations, which contribute to the suppression of long–range order in both materials in the same way, the random fields due to isomer disorder that exist in Mn_{12}–ac and not in Mn_{12}–ac–MeOH causes further suppression of ferromagnetism in Mn_{12}–ac. The behavior observed for Mn_{12}–ac is consistent with a random field model calculated for this system by Millis et al.### Time Reversal Optical Tomography and Decomposition Methods for Detection and Localization of Targets in Highly Scattering Turbid Media

Author:Binlin WuYear of Dissertation:2013Program:PhysicsAdvisor:Swapan GayenAbstract:New near-infrared (NIR) diffuse optical tomography (DOT) approaches were developed to detect, locate, and image small targets embedded in highly scattering turbid media. The first approach, referred to as time reversal optical tomography (TROT), is based on time reversal (TR) imaging and multiple signal classification (MUSIC). The second approach uses decomposition methods of non-negative matrix factorization (NMF) and principal component analysis (PCA) commonly used in blind source separation (BSS) problems, and compare the outcomes with that of optical imaging using independent component analysis (OPTICA). The goal is to develop a safe, affordable, noninvasive imaging modality for detection and characterization of breast tumors in early growth stages when those are more amenable to treatment. The efficacy of the approaches was tested using simulated data, and experiments involving model media and absorptive, scattering, and fluorescent targets, as well as, "realistic human breast model" composed of

ex vivo breast tissues with embedded tumors. The experimental arrangements realized continuous wave (CW) multi-source probing of samples and multi-detector acquisition of diffusely transmitted signal in rectangular slab geometry. A data matrix was generated using the perturbation in the transmitted light intensity distribution due to the presence of absorptive or scattering targets. For fluorescent targets the data matrix was generated using the diffusely transmitted fluorescence signal distribution from the targets. The data matrix was analyzed using different approaches to detect and characterize the targets. The salient features of the approaches include ability to: (a) detect small targets; (b) provide three-dimensional location of the targets with high accuracy (~within a millimeter or 2); and (c) assess optical strength of the targets. The approaches are less computation intensive and consequently are faster than other inverse image reconstruction methods that attempt to reconstruct the optical properties of every voxel of the sample volume. The location of a target was estimated to be the weighted center of the optical property of the target. Consequently, the locations of small targets were better specified than those of the extended targets. It was more difficult to retrieve the size and shape of a target. The fluorescent measurements seemed to provide better accuracy than the transillumination measurements. In the case ofex vivo detection of tumors embedded in human breast tissue, measurements using multiple wavelengths provided more robust results, and helped suppress artifacts (false positives) than that from single wavelength measurements. The ability to detect and locate small targets, speedier reconstruction, combined with fluorophore-specific multi-wavelength probing has the potential to make these approaches suitable for breast cancer detection and diagnosis.### RENORMALIZATION OF QCD UNDER LONGITUDINAL RESCALING

Author:JING XIAOYear of Dissertation:2009Program:PhysicsAdvisor:Peter OrlandAbstract:Under a longitudinal rescaling of coordinates x

0,3 → λ x0,3 , λ << 1, the classical QCD action simplifies dramatically. This is the high-energy limit, as λ ∼ s-1/2 where s is the center-of-mass energy squared of a hadronic collision. We find the quantum corrections to the rescaled action at one loop, in particular finding the anomalous powers of λ in this action, with λ < 1. The method is an integration over high-momentum components of the gauge field. This is a Wilsonian renormalization procedure, and counterterms are needed to make the sharp-momentum cut-off gauge invariant. Our result for the quantum action is found, assuming |lnλ| << 1, which is essential for the validity of perturbation theory. If λ is sufficiently small (so that |lnλ| >> 1), then the perturbative renormalization group breaks down. This is due to uncontrollable fluctuations of the longitudinal chromomagnetic field.### Crystal Growth and Neutron Scattering Studies of High Temperature Superconductors

Author:Zhijun XuYear of Dissertation:2011Program:PhysicsAdvisor:Jiufeng TuAbstract:Since the discovery of the first high temperature superconductor in the 1980's, there have been continuing efforts to understand the mechanism of high-T

_{C}superconductivity. Studies on the cuprate systems seem to suggest that there is an intimate relationship between superconductivity and magnetism, and recently this has also shown to be the case for the newly discovered Fe-based superconductors. Neutron scattering is a powerful tool for studying magnetism in superconductors, which can provide important information about the momentum and energy dependence of magnetic correlations. The work presented in this thesis is divided into two main sections. Since high-quality large-size single crystals are necessary for the neutron scattering experiments. The first section is about sample preparation, where I will introduce single crystal growths via the Floating-zone technique as well as unidirectional solidi¯cation methods. The second section is neutron scattering experiments, which will show neutron scattering and transport measurements results in two high-temperature superconductor systems: La_{2-x}Ba_{x}CuO_{4}(LBCO), and Fe_{1+y}Te_{1-x}Se_{x}(FeTeSe). In the LBCO system, we found that static magnetic order competes with bulk superconductivity. In addition, applying a magnetic field to or adding Zn impurities in the sample will enhance the static magnetic order and suppress the superconductivity. In the FeTeSe system, we found that spin resonance is associated with superconductivity, while resonance and superconductivity are simultaneously suppressed by an applied magnetic field or adding Fe impurities. Our results suggest that the magnetic correlations are important for the superconductivity, and proper tuning of these correlations may be a key for superconductivity.### A Classical And Quantum Noise Model

Author:Yejun YangYear of Dissertation:2009Program:PhysicsAdvisor:Leon CohenAbstract:We develop detailed statistics of a noise model that consists of $N$ independent harmonic oscillators where the total force is given by the sum of the individual forces. This model was first proposed in the paper by Ford, Kac, and Mazur that was aimed at deriving the Langevin equation from first principles. We extend the model and calculate relevant probability distributions and other statistical quantities such as the autocorrelation function. In the usual model one assumes that the initial position and momentum values are stochastic variables that determine the statistical features of the force by ensemble averaging over those quantities. We extend that by also treating the mass and frequency as statistical quantities. We consider both the equilibrium case, that is the canonical distribution for the initial positions and momenta, for the but we also consider other initial distributions and show that this leads to non-stationary autocorrelation functions. One of our basic aims is to also develop this model for the quantum case and compare the results with the classical case. The general approach we use for the calculation of the statistical quantities is by way of the characteristic function. We use the characteristic function approach because the oscillators are independent of each other. However, the quantum characteristic function present unique difficulties because the initial momentum and position operators do not commute. We use the Weyl correspondence to define the quantum characteristic function and we derive explicit expressions for both the pure case and mixtures. We show that many of the statistical quantities can be expressed in terms of the Wigner distribution. In addition, we consider the time-frequency Wigner spectrum of momentum governed by the Langevin equation when the random driving term is quantum noise. We obtaine an explicit equation. The equation is solved exactly and includes both the transient and the stationary part. The time-dependent Wigner spectrum generalizes the result of Wang and Uhlenbeck wherein they showed that for the white noise driving force the power spectrum in the stationary state regime is Lorenzian. We show that our solution reduces to the classical solution when the parameters of the quantum noise are such that the white noise limit is approached and when the long time limit is taken.

### EXPLORATION OF CsSnI3: UNCOVERING OPTICAL AND ELECTRICAL PROPERTIES FOR PHOTONIC DEVICE APPLICATIONS

Author:Chonglong YuYear of Dissertation:2013Program:PhysicsAdvisor:Kai ShumAbstract:This thesis is about the exploration of the optical properties of perovskite compound CsSnI3 (CSI), a newly identified semiconductor material. Based on what have been discovered so far, we believe that it has a great potential for photonic device applications. The exploration starts with the determination of the atomic and electronic structures of CSI and continues with the fundamental understanding of the optical properties revealed by spectroscipic measurments. One of the most fascinating optical properties associated with the unique atomic structuture of CSI is the superfluorecence from the correlated two-dimensional excitons naturally formed in the planes of SnI4 tetragons. After a brief introduction on the prior and recent research activities on CSI, the atomic structures and structural phase transitions of CSI were investigated using the first-principles approach. With the detailed structural information, the full electronic eigen states of CSI in its phase, commonly accessible by the full optical spectrum from near infrared to ultraviolet, have been calculated. A few key charcteristics of the electronic structure were identified and discussed in view of their optical consequences, such as the much larger effective mass of electrons than that of holes, and the existence of the two lowest parallel conduction bands with an energy separation of 64 meV. In the chapters of 4, 5 and 6, the exploration continues with the understanding of interesting optical properties and the associated physics processes. The abnormal temperature dependence of the energy band gap of CSI is explained by the two combined effects: 1) the neglegible contribution of direct electron-phonon interactions to the band gap change due to the unusual large electron effective mass, and 2) the positive thermal expansion effect to the band gap change calculated by the first-principle approach. Pronounced two-LO-phonon features in both Raman scattering and photoluminescence excitation spectra are interpreted as the resonantly enhanced two-LO-phonon emission processes, originated by the unique electronic band structure of CSI: the two lowest parallel conduction bands with the energy separation close to the energy of two LO phonons. The final part of my thesis in the chapters of 7 and 8 is devoted to the one of most exciting and abstruse phenomena in photonics: superfluorescence (SF). After revisiting Dicke's initial superradiance theory and combining the characteristics of SF, we have developed a model to capture the essential physics, especially on the dynamic time evolution of SF. This model predicts the bi-exponential decay behavior when considerable dephasing is present. Meanwhile, the intensity of SF burst, delay time, and decay rate are also studied with the model. The SF in CSI is revealed through the power and temperature dependences of time resolved photoluminescence. The measured photoluminescence characteristics are shown to match all the SF features predicted by our model, such as the bi-exponential decay, the inverse relation of delay time over the number of exciton (N), the linear relation of decay rate over N, and the temperature dependence of decay rate. The natural formation of two dimensional excitons in the parallel planes of SnI4 tetragons is argued to be the reason for the SF to occur in CSI.

### Engineering cofactor and ligand binding in an artificial neuroglobin

Author:Lei ZhangYear of Dissertation:2012Program:PhysicsAdvisor:Ronald KoderAbstract:HP-7 is one artificial mutated oxygen transport protein, which operates via a mechanism akin to human neuroglobin and cytoglobin. This protein destabilizes one of two heme- ligating histidine residues by coupling histidine side chain ligation with the burial of three charged glutamate residues on the same helix. Replacement of these glutamate residues with alanine, which has a neutral hydrophobicity, slows gaseous ligand binding 22-fold, increases the affinity of the distal histidine ligand by a factor of thirteen, and decreases the binding affinity of carbon monoxide, a nonreactive oxygen analogue, three-fold. Paradoxically, it also decreases heme binding affinity by a factor of three in the reduced state and six in the oxidized state. Application of a two-state binding model, in which an initial pentacoordinate binding event is followed by a protein conformational change to hexacoordinate, provides insight into the mechanism of this seemingly counterintuitive result: the initial pentacoordinate encounter complex is significantly destabilized by the loss of the glutamate side chains, and the increased affinity for the distal histidine only partially compensates. These results point to the importance of considering each oxidation and conformational state in the design of functional artificial proteins. We have also examined the effects these mutations have on function. The Kd of the nonnreactive oxygen analogue carbon monoxide (CO) is only decreased three-fold, despite the large increase in distal histidine affinity engendered by the 22-fold decrease in the histidine ligand off-rate. This is a result of the four-fold increase in affinity for CO binding to the pentacoordinate state. Oxygen binds to HP7 with a Kd of 117 µM, while the mutant rapidly oxidizes when exposed to oxygen. EPR analysis of both ferric hemoproteins demonstrates that the mutation increases disorder at the heme binding site. NMR-detected deuterium exchange demonstrates that the mutation causes a large increase in water penetration into the protein core. The inability of the mutant protein may thus either be due to increased water penetration, the large decrease in binding rate caused by the increase in distal histidine affinity, or a combination of the two factors.