Physics Department Theses and Dissertations

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The Effect of Acyl Chain Unsaturation on Phospholipid Bilayer
(2010-02-26T17:51:02Z) Soni, Smita Pravin; Wassall, Stephen R.; Petrache, Horia; Kemple, Marvin D.; Rader, Andrew J.
Each biological cell is surrounded by a membrane that consists of many different kinds of lipids. The lipids are mainly composed of phospholipids, which form a fluid bilayer that serves as the platform for the function of membrane bound proteins regulating cellular activity. In the research described in this thesis we employed solid state 2H NMR, complemented by DSC (differential scanning calorimetry) and MD (molecular dynamics) simulations, to study the effect of PUFA (polyunsaturated fatty acids) and TFA (trans fatty acids) on molecular organization in protein-free model membranes of controlled composition. These two classes of unsaturated fatty acid incorporate into membrane lipids and have, respectively, a beneficial and harmful impact on health. The aim is to gain insight into the molecular origin of this behavior. DHA (docosahexaenoic acid), which with 6 "natural" cis double bonds is the most highly unsaturated PUFA found in fish oils, and EA (elaidic acid), which with only a single "unnatural" trans double bond is the simplest manmade TFA often found in commercially produced food, were the focus. 2H NMR spectra for [2H31]-N-palmitoylsphingomyelin ([2H31]16:0SM) in SM/16:0-22:6PE (1-palmitoyl-2-docosahexaenoylphosphatidylethanolamine)/cholesterol (1:1:1 mol) mixed membranes were recorded. This system served as our PUFA-containing model. The spectra are consistent with lateral separation into nano-sized (< 20 nm) domains that are SM-rich/cholesterol-rich (raft), characterized by higher chain order, and DHA-rich/cholesterol-poor (non-raft), characterized by lower chain order. The aversion cholesterol has for DHA, as opposed to the affinity cholesterol has for predominantly saturated SM, excludes the sterol from DHA-containing PE-rich domains and DHA from SM-rich/cholesterol-rich domains. It is the formation of highly disordered membrane domains that we hypothesize is responsible, in part, for the diverse health benefits associated with dietary consumption of DHA. 2H NMR spectra for 1-elaidoyl-2-[2H35]stearoylphosphatidylcholine (t18:1-[2H35]18:0PC) and 1-oleoyl-2-[2H35]stearoylphosphatidylcholine (c18:1-[2H35]18:0PC) were recorded to compare membranes with respect to a trans vs. cis ("natural") double bond. The spectra indicate that while a trans double bond produces a smaller deviation from linear conformation than a cis double bond, membrane order is decreased by a comparable amount because the energy barrier to rotation about the C-C single bonds either side of a trans or cis double bond is reduced. Although EA adopts a conformation somewhat resembling a saturated fatty acid, the TFA is almost as disordered as its cis counterpart oleic acid (OA). We speculate that EA could be mistaken for a saturated fatty acid and infiltrate lipid rafts to disrupt the high order therein that is necessary for the function of signaling proteins.
Lattice and Momentum Space Approach to Bound States and Excitonic Condensation via User Friendly Interfaces
(2012-03-20) Jamell, Christopher Ray; Joglekar, Yogesh; Decca, Ricardo; Nageswara Rao, B. D.; Cheng, Ruihua; Hu, Jiangping
In this thesis, we focus on two broad categories of problems, exciton condensation and bound states, and two complimentary approaches, real and momentum space, to solve these problems. In chapter 2 we begin by developing the self-consistent mean field equations, in momentum space, used to calculate exciton condensation in semiconductor heterostructures/double quantum wells and graphene. In the double quantum well case, where we have one layer containing electrons and the other layer with holes separated by a distance $d$, we extend the analytical solution to the two dimensional hydrogen atom in order to provide a semi-quantitative measure of when a system of excitons can be considered dilute. Next we focus on the problem of electron-electron screening, using the random phase approximation, in double layer graphene. The literature contains calculations showing that when screening is not taken into account the temperature at which excitons in double layer graphene condense is approximately room temperature. Also in the literature is a calculation showing that under certain assumptions the transition temperature is approximately \unit{mK}. The essential result is that the condensate is exponentially suppressed by the number of electron species in the system. Our mean field calculations show that the condensate, is in fact, not exponentially suppressed. Next, in chapter 3, we show the use of momentum space to solve the Schr\"{o}dinger equation for a class of potentials that are not usually a part of a quantum mechanics courses. Our approach avoids the typical pitfalls that exist when one tries to discretize the real space Schr\"{o}dinger equation. This technique widens the number of problems that can presented in an introductory quantum mechanics course while at the same time, because of the ease of its implementation, provides a simple introduction to numerical techniques and programming in general to students. We have furthered this idea by creating a modular program that allows students to choose the potential they wish to solve for while abstracting away the details of how the solution is found. In chapter 4 we revisit the single exciton and exciton condensation in double layer graphene problems through the use of real space lattice models. In the first section, we once again develop the equations needed to solve the problem of exciton condensation in a double layer graphene system. In addition to this we show that by using this technique, we find that for a non-interacting system with a finite non-zero tunneling between the layers that the on-site exciton density is proportional to the tunneling amplitude. The second section returns to the single exciton problem. In agreement with our momentum space calculations, we find that as the layer separation distance is increased the bound state wave function broadens. Finally, an interesting consequence of the lattice model is explored briefly. We show that for a system containing an electron in a periodic potential, there exists a bound state for both an attractive as well as repulsive potential. The bound state for the repulsive potential has as its energy $-E_0$ where $E_0$ is the ground state energy of the attractive potential with the same strength.
Near-Field Investigations of the Anisotropic Properties of Supported Lipid Bilayers
(2012-07-24) Johnson, Merrell A.; Decca, Ricardo; Rader, Andrew J.; Ritchie, Ken; Petrache, Horia; Wassall, Stephen
The details of Polarization Modulation Near-Field Scanning Optical Microscopy (PM-NSOM) are presented. How to properly calibrate and align the system is also introduced. A measurement of Muscovite crystal is used to display the capabilities of the setup. Measurements of supported Lβʹ 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayers are presented, emphasizing how it was tooled in exploiting the anisotropic nature of the acyl chains. A discussion of how the effective retardance (ΔS = 2π( n_e-n_o )t/λ) and the direction of the projection of the acyl chains (θ) are measured simultaneously is given, (where t is the thickness of the bilayer and λ is the wavelength of light used). It is shown from ΔS the birefringence (ne-no) of the bilayer is determined, by assuming the acyl chain tilt with respect to the membrane's normal to be ϕ ≈ 32. Time varying experiments show lateral diffusions of ~ 2 x 10-12 cm2/s. Temperature controlled PM-NSOM is shown to be a viable way to determine the main phase transition temperature (Tm) for going from the gel Lβʹ to liquid disorder Lα state of supported DPPC bilayers. A change of ΔS ~ (3.8 +/- 0.3 mrad) at the main phase transition temperature Tm (≈41^o C) is observed. This agrees well with previous values of (ne-no) and translates to an assumed <ϕ> ~ 32^o when T < Tm and 0^o when T > Tm. Evidence of supper heating and supper cooling will be presented, along with a discussion of the fluctuations that occur around Tm. Finally it is shown how physical parameters such as the polarizability are extracted from the data. Values of the transverse (αt) and longitudinal (αl) polarizabilites of the acyl chains are shown to be, αt = 44.2 Å3 and αl = 94.4 Å3, which correspond well with the theoretical values of a single palmitic acid (C16) αt = 25.14 Å3 and αl = 45.8 Å3.
Characterization and Measurement of Hybrid Gas Journal Bearings
(2012-08-28) Lawrence, Tom Marquis; Kemple, Marvin D.; Decca, Ricardo; Joglekar, Yogesh; Petrache, Horia; Akay, Hassan; Krousgrill, Charles Morton
This thesis concentrates on the study of hybrid gas journal bearings (bearings with externally pressurized mass addition). It differs from most work in that it goes back to “basics” to explore the hydrodynamic phenomena in the bearing gap. The thesis compares geometrically identical bearings with 2 configurations of external pressurization, porous liners where mass-addition compensation is varied by varying the liner’s permeability, and bushings with 2 rows of 6 feedholes where the mass-addition compensation is varied by the feedhole diameter. Experimentally, prototype bearings with mass-addition compensation that spans 2 orders of magnitude with differing clearances are built and their aerostatic properties and mass addition characteristics are thoroughly tested. The fundamental equations for compressible, laminar, Poiseuille flow are used to suggest how the mass flow “compensation” should be mathematically modeled. This is back-checked against the experimental mass flow measurements and is used to determine a mass-addition compensation parameter (called Kmeas) for each prototype bushing. In so doing, the methodology of modeling and measuring the mass addition in a hybrid gas bearing is re-examined and an innovative, practical, and simple method is found that makes it possible to make an “apples-to-apples” comparison between different configurations of external pressurization. This mass addition model is used in conjunction with the Reynolds equation to perform theory-based numerical analysis of virtual hybrid gas journal bearings (CFD experiments). The first CFD experiments performed use virtual bearings modeled to be identical to the experimental prototypes and replicate the experimental work. The results are compared and the CFD model is validated. The ontological significance of appropriate dimensionless similitude parameters is re-examined and a, previously lacking, complete set of similitude factors is found for hybrid bearings. A new practical method is developed to study in unprecedented detail the aerostatic component of the hybrid bearings. It is used to definitively compare the feedhole bearings to the porous liner bearings. The hydrostatic bearing efficiency (HBE) is defined and it is determined that the maximum achievable hydrostatic bearing efficiency (MAHBE) is determined solely by the bearing’s mass addition configuration. The MAHBE of the porous liner bearings is determined to be over 5 times that of the feedhole bearings. The method also presents a means to tune the Kmeas to the clearance to achieve the MAHBE as well as giving a complete mapping of the hitherto misunderstood complex shapes of aerostatic load versus radial deflection curves. This method also rediscovers the obscure phenomenon of static instability which is called in this thesis the “near surface effect” and appears to be the first work to present a practical method to predict the range of static instability and quantify its resultant stiffness fall-off. It determines that porous liner type bearings are not subject to the phenomenon which appears for feedhole type bearings when the clearance exceeds a critical value relative to its mass-addition compensation. The standing pressure waves of hydrostatic and hybrid bearings with the 2 configurations of external pressurization as well as a geometrically identical hydrodynamic bearing are studied in detail under the methodology of the “CFD microscope”. This method is used to characterize and identify the development, growth, and movement of the pressure wave extrema with increased hydrodynamic action (either increasing speed or increasing eccentricity). This method is also used to determine the “cause” of the “near surface effect”. A gedanken experiment is performed based on these results which indicates that a bearing with a “stronger aerostatic strength” component should be more stable than one with a low aerostatic strength component. Numerical instability “speed limits” are found that are also related to the hydrostatic strength of the bearing. The local conditions in the standing waves are characterized in terms of their local Mach number, Knudsen number, Reynolds number, and Taylor Number. It is concluded that low eccentricity bearing whirl can be attributed to the off load-line orientation of the bearing load force caused by the overlay of the hydrodynamic bearing standing wave onto the hydrostatic bearing wave of the hybrid bearing, whereas it is hypothesized that aperiodic and random self-excited vibration which occurs at high eccentricity, as reported in the literature, is probably due to shock waves, turbulence, near surface effect, and slip at local areas of the standing wave.
Biophysical studies of cholesterol in unsaturated phospholipid model membranes
(2013) Williams, Justin A.; Wassall, Stephen R.; Decca, Ricardo; Petrache, Horia; Zhu, Fangqiang; Todd, Brian A.
Cellular membranes contain a staggering diversity of lipids. The lipids are heterogeneously distr ibuted to create regions, or domains, whose physical properties differ from the bulk membrane and play an essential role in modulating the function of resident proteins. Many basic questions pertaining to the formation of these lateral assemblies remain. T his research employs model membranes of well - defined composition to focus on the potential role of polyunsaturated fatty acids (PUFAs) and their interaction with cholesterol (chol) in restructuring the membrane environment. Omega - 3 (n - 3) PUFAs are the main bioactive components of fish oil, whose consumption alleviates a variety of health problems by a molecular mechanism that is unclear. We hypothesize that the incorporation of PUFAs into membrane lipids and the effect they have on molecular organization may be, in part, responsible. Chol is a major constituent in the plasma membrane of mammals. It determines the arrangement and collective properties of neighboring lipids, driving the formation of domains via differential affinity for different lipids . T he m olecular organization of 1 -[ 2 H 31 ]palmitoyl -2- eicosapentaenoylphosphatidylcholine (PEPC - d 31 ) and 1 -[ 2 H 31 ]palmitoyl -2- docosahexaenoylphosphatidylcholine (PDPC -d 31 ) in membran es with sphingomyelin (SM) and chol (1:1:1 mol) was compared by solid - state 2 H NMR spectroscopy. Eicosapentaenoic (EPA) and docosahexaenoic (DHA) acids are the two major n - 3 PUFAs found in fish oil, while PEPC -d 31 and PDPC -d 31 are phospholipids containing the respective PUFAs at the sn - 2 position and a perdeuterated palmitic acid a t the sn - 1 position . Analysis of s pectra recorded as a function of temperature indicate s that in both cases, formation of PUFA - rich (less ordered) and SM - rich (more ordered) domains occurred. A surprisingly substantial proportion of PUFA was found to infil trate the more ordered domain. There was almost twice as much DHA (65%) as EPA (30%) . The implication is that n - 3 PUFA s can incorporate into lipid rafts, which are domains enriched in SM and chol in the plasma membrane, and potentially disrupt the activity of signaling proteins that reside therein. DHA, furthermore, may be the more potent component of fish oil. PUFA - chol interactions were also examined through affinity measurements. A novel method utilizing electron paramagnetic resonance (EPR) was develope d, to monitor the partitioning of a spin - labeled analog of chol , 3β - doxyl - 5α - cholestane (chlstn), between large unilamellar vesicles (LUVs) and met hyl - β - cyclodextrin (mβCD). The EPR spectra for chlstn in the two environments are distinguishable due to the substantial differences in tumbling rates , allowing the population distribution ratio to be determined by spectral simulation. Advantages of this approach include speed of implementation and a vo idance of potential artifact s associated with physical separation of LUV and mβCD . Additionally, in a check of the method, t he relative partition coefficients between lipids measured for the spin label analog agree with values obtained for chol by isothermal titration calorimetry (ITC). Results from LUV with different composition confirmed a hierarchy of decreased sterol affinity for phospholipids with increasing acyl chain unsaturation , PDPC possessing half the affinity of the corresponding monounsaturated phospholipid. Taken together, the results of these studies on model membranes demonstrate the potential for PUFA - driven alteration of the architecture of biomembranes, a mechanism through which human health may be impacted.
INVESTIGATION OF QUANTUM FLUCTUATIONS IN A NONLINEAR INTERFEROMETER WITH HARMONIC GENERATION AND COHERENT INTERACTION OF LIGHT AND CS ATOMS
(2013-08-23) Srinivasan, Prashant; Ou, Zhe-Yu Jeff; Decca, Ricardo; Vemuri, Gautam; Petrache, Horia
In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.
Reactive oxygen species' role in endothelial dysfunction by electron paramagnetic resonance
(2013-08-29) Wassall, Cynthia D.; Kemple, Marvin D.; Joglekar, Yogesh; Petrache, Horia; Nageswara Rao, B. D.; Durbin, Stephen M.; Decca, Ricardo
The endothelium is a single layer of cells lining the arteries and is involved in many physiological reactions which are responsible for vascular tone. Free radicals are important participants in these chemical reactions in the endothelium. Here we quantify free radicals, ex vivo, in biological tissue with continuous wave electron paramagnetic resonance (EPR). In all of the experiments in this thesis, we use a novel EPR spin trapping technique that has been developed for tissue segments. EPR spin trapping is often considered the ‘gold standard’ in reactive oxygen species (ROS) detection because of its sensitivity and non-invasive nature. In all experiments, tissue was placed in physiological saline solution with 190-mM PBN (N-tert-butyl-α-phenylnitrone), 10% by volume dimethyl-sulphoxide (DMSO) for cryopreservation, and incubated in the dark for between 30 minutes up to 2 hours at 37°C while gently being stirred. Tissue and supernatant were then loaded into a syringe and frozen at -80°C until EPR analysis. In our experiments, the EPR spectra were normalized with respect to tissue volume. Conducting experiments at liquid nitrogen temperature leads to some experimental advantages. The freezing of the spin adducts renders them stable over a longer period, which allows ample time to analyze tissue samples for ROS. The dielectric constant of ice is greatly reduced over its liquid counterpart; this property of water enables larger sample volumes to be inserted into the EPR cavity without overloading it and leads to enhanced signal detection. Due to Maxwell-Boltzmann statistics, the population difference goes up as the temperature goes down, so this phenomenon enhances the signal intensity as well. With the ‘gold standard’ assertion in mind, we investigated whether slicing tissue to assay ROS that is commonly used in fluorescence experiments will show more free radical generation than tissue of a similar volume that remains unsliced. Sliced tissue exhibited a 76% increase in ROS generation; this implies that higher ROS concentrations in sliced tissue indicate extraneous ROS generation not associated with the ROS stimulus of interest. We also investigated the role of ROS in chronic flow overload (CFO). Elevation of shear stress that increases production of vascular ROS has not been well investigated. We hypothesize that CFO increases ROS production mediated in part by NADPH oxidase, which leads to endothelial dysfunction. ROS production increased threefold in response to CFO. The endothelium dependent vasorelaxation was compromised in the CFO group. Treatment with apocynin significantly reduced ROS production in the vessel wall, preserved endothelial function, and inhibited expressions of p22/p47phox and NOX2/NOX4. The present data implicate NADPH oxidase produced ROS and eNOS uncoupling in endothelial dysfunction at 1 wk of CFO. In further work, a swine right ventricular hypertrophy (RVH) model induced by pulmonary artery (PA) banding was used to study right coronary artery (RCA) endothelial function and ROS level. Endothelial function was compromised in RCA of RVH as attributed to insufficient endothelial nitric oxide synthase cofactor tetrahydrobiopterin. In conclusion, stretch due to outward remodeling of RCA during RVH (at constant wall shear stress), similar to vessel stretch in hypertension, appears to induce ROS elevation, endothelial dysfunction, and an increase in basal tone. Finally, although hypertension-induced vascular stiffness and dysfunction are well established in patients and animal models, we hypothesize that stretch or distension due to hypertension and outward expansion is the cause of endothelial dysfunction mediated by angiotensin II type 1 (AT1) receptor in coronary arteries. The expression and activation of AT1 receptor and the production of ROS were up regulated and endothelial function deteriorated in the RCA. The acute inhibition of AT1 receptor and NADPH oxidase partially restored the endothelial function. Stretch or distension activates the AT1 receptor which mediates ROS production; this collectively leads to endothelial dysfunction in coronary arteries.
Induced magnetoelectric coupling at a ferroelectric-ferromagnetic interface
(2013-11-08) Carvell, Jeffrey David; Ruihua, Cheng; Joglekar, Yogesh; Decca, Ricardo; Petrache, Horia; Hu, Jiangping
Preparation and characterization of multiferroic materials in which ferroelectricity and ferromagnetism coexist would be a milestone for functionalized materials and devices. First, electric properties of polyvinylidene (PVDF) films fabricated using the Langmuir-Schaefer method have been studied. Films of different thickness were deposited on silicon substrates and analyzed using several techniques. X-ray diffraction (XRD) data showed that PVDF films crystallize at an annealing temperature above 130 °C. Polarization versus electric field (PE) ferroelectric measurements were done for samples prepared with electrodes. PE measurements show that the coercivity of the films increases as the maximum applied electric field increases. The coercivity dependence on the frequency of the applied electric field can be fitted as . The results also show that the coercivity decreases with increasing the thickness of PVDF film due to the pinning effect. Next, we have demonstrated that those PVDF properties can be controlled by applying an external magnetic field. Samples were created in a layered heterostructure, starting with a Fe thin film, PVDF above that, and followed by another thin film of Fe. Extended X-ray absorption fine structure (EXAFS) spectroscopy was used to study the interface between PVDF polymer films and ferromagnetic iron thin films. Conventional EXAFS was applied to identify the structure of a Fe film sandwiched between two PVDF layers. An electric signal was then applied to the polymer to study the effects polarizing the polymer has on the Fe atoms at the interface. This shows that the Fe atoms diffuse into the PVDF layer at the interface between the two layers. Polarizing the film causes further diffusion of Fe atoms into the polymer. We also found that as the applied magnetic field is changed, the switching of electric polarization for the PVDF displayed a dependence on the external magnetic field. We also noticed that both the coercivity and polarization for the PVDF polymer display hysteretic features as the applied magnetic field is changed. We also found that the thickness of both the iron layers and the PVDF layer has an effect on the magnetoelectric coupling in our samples. The same strain applied to a thicker PVDF layer becomes tougher to flip the polarization compared to a thinner PVDF layer. As the iron film thickness increases, the strain also increases, and the polarization of the PVDF polymer is more easily flipped. We also found that the magnetoelectric sensitivity increases as both the PVDF and iron layers increase in thickness. We have shown that it is possible to control the ferroelectric properties of a PVDF film by tuning the magnetic field in a heterostructure. Our experiments show a coupling between the electric polarization and applied magnetic field in multiferroic heterostructures much larger than any previously reported values. Previous reports have used inorganic materials for the ferroelectric layer. Organic polymers have an electric dipole originating at the molecular level due to atoms with different electronegativity that are free to rotate. To flip the polarization, the chains must rotate and the position of the atoms must change. This increases the force felt locally by those chains. Using this polymer, we are able to increase the magnetoelectric coupling.
Quantum physics inspired optical effects in evanescently coupled waveguides
(2014) Thompson, Clinton Edward; Vemuri, Gautam; Joglekar, Yogesh; Nolte, D. D.; Decca, Ricardo; Ou, Zhe-Yu Jeff
The tight-binding model that has been used for many years in condensed matter physics, due to its analytic and numerical tractability, has recently been used to describe light propagating through an array of evanescently coupled waveguides. This dissertation presents analytic and numerical simulation results of light propagating in a waveguide array. The first result presented is that photonic transport can be achieved in an array where the propagation constant is linearly increasing across the array. For an input at the center waveguide, the breathing modes of the system are observed, while for a phase displaced, asymmetric input, phase-controlled photonic transport is predicted. For an array with a waveguide-dependent, parity-symmetric coupling constant, the wave packet dynamics are predicted to be tunable. In addition to modifying the propagation constant, the coupling between waveguides can also be modified, and the quantum correlations are sensitive to the form of the tunneling function. In addition to modifying the waveguide array parameters in a structured manner, they can be randomized as to mimic the insertion of impurities during the fabrication process. When the refractive indices are randomized and real, the amount of light that localizes to the initial waveguide is found to be dependent on the initial waveguide when the waveguide coupling is non-uniform. In addition, when the variance of the refractive indices is small, light localizes in the initial waveguide as well as the parity-symmetric waveguide. In addition to real valued disorder, complex valued disorder can be introduced into the array through the imaginary component of the refractive index. It is shown that the two-particle correlation function is qualitatively similar to the case when the waveguide coupling is real and random, as both cases preserve the symmetry of the eigenvalues. Lastly, different input fields have been used to investigate the quantum statistical aspects of Anderson localization. It is found that the fluctuations in the output intensity are enhanced and the entropy of the system is reduced when disorder is present in the waveguides.
An investigation of parity and time-reversal symmetry breaking in tight-binding lattices
(2014) Scott, Derek Douglas; Joglekar, Yogesh; Decca, Ricardo; Petrache, Horia; Tarasov, Vitaly; Csathy, Gabor
More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the effects of PT symmetry breaking in systems as diverse as coupled mechanical pendula, coupled optical waveguides, and coupled electrical circuits. Recently, PT -symmetric Hamiltonians for tight-binding lattice models have been extensively investigated. Lattice models, in general, have been widely used in physics due to their analytical and numerical tractability. Perhaps one of the best systems for experimentally observing the effects of PT symmetry breaking in a one-dimensional lattice with tunable hopping is an array of evanescently-coupled optical waveguides. The tunneling between adjacent waveguides is tuned by adjusting the width of the barrier between them, and the imaginary part of the local refractive index provides the loss or gain in the respective waveguide. Calculating the time evolution of a wave packet on a lattice is relatively straightforward in the tight-binding model, allowing us to make predictions about the behavior of light propagating down an array of PT -symmetric waveguides. In this thesis, I investigate the the strength of the PT -symmetric phase (the region over which the eigenvalues are purely real) in lattices with a variety of PT - symmetric potentials. In Chapter 1, I begin with a brief review of the postulates of quantum mechanics, followed by an outline of the fundamental principles of PT - symmetric systems. Chapter 2 focuses on one-dimensional uniform lattices with a pair of PT -symmetric impurities in the case of open boundary conditions. I find that the PT phase is algebraically fragile except in the case of closest impurities, where the PT phase remains nonzero. In Chapter 3, I examine the case of periodic boundary conditions in uniform lattices, finding that the PT phase is not only nonzero, but also independent of the impurity spacing on the lattice. In addition, I explore the time evolution of a single-particle wave packet initially localized at a site. I find that in the case of periodic boundary conditions, the wave packet undergoes a preferential clockwise or counterclockwise motion around the ring. This behavior is quantified by a discrete momentum operator which assumes a maximum value at the PT -symmetry- breaking threshold. In Chapter 4, I investigate nonuniform lattices where the parity-symmetric hop- ping between neighboring sites can be tuned. I find that the PT phase remains strong in the case of closest impurities and fragile elsewhere. Chapter 5 explores the effects of the competition between localized and extended PT potentials on a lattice. I show that when the short-range impurities are maximally separated on the lattice, the PT phase is strengthened by adding short-range loss in the broad-loss region. Consequently, I predict that a broken PT symmetry can be restored by increasing the strength of the short-range impurities. Lastly, Chapter 6 summarizes my salient results and discusses areas which can be further developed in future research.

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