ASU Scholarship Showcase

Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.

The phenomenon of Fano resonance is ubiquitous in a large variety of wave scattering systems, where the resonance profile is typically asymmetric. Whether the parameter characterizing the asymmetry should be complex or real is an issue of great experimental interest. Using coherent quantum transport as a paradigm and taking into account of the collective contribution from all available scattering channels, we derive a universal formula for the Fano-resonance profile. We show that our formula bridges naturally the traditional Fano formulas with complex and real asymmetry parameters, indicating that the two types of formulas are fundamentally equivalent (except for an offset). The connection also reveals a clear footprint for the conductance resonance during a dephasing process. Therefore, the emergence of complex asymmetric parameter when fitting with experimental data needs to be properly interpreted. Furthermore, we have provided a theory for the width of the resonance, which relates explicitly the width to the degree of localization of the close-by eigenstates and the corresponding coupling matrices or the self-energies caused by the leads. Our work not only resolves the issue about the nature of the asymmetry parameter, but also provides deeper physical insights into the origin of Fano resonance. Since the only assumption in our treatment is that the transport can be described by the Green’s function formalism, our results are also valid for broad disciplines including scattering problems of electromagnetic waves, acoustics, and seismology.

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

Most previous works on complete synchronization of chaotic oscillators focused on the one-channel interaction scheme where the oscillators are coupled through only one variable or a symmetric set of variables. Using the standard framework of master-stability function (MSF), we investigate the emergence of complex synchronization behaviors under all possible configurations of two-channel coupling, which include, for example, all possible cross coupling schemes among the dynamical variables. Utilizing the classic Rössler and Lorenz oscillators, we find a rich variety of synchronization phenomena not present in any previously extensively studied, single-channel coupling configurations. For example, in many cases two coupling channels can enhance or even generate synchronization where there is only weak or no synchronization under only one coupling channel, which has been verified in a coupled neuron system. There are also cases where the oscillators are originally synchronized under one coupling channel, but an additional synchronizable coupling channel can, however, destroy synchronization. Direct numerical simulations of actual synchronization dynamics verify the MSF-based predictions. Our extensive computation and heuristic analysis provide an atlas for synchronization of chaotic oscillators coupled through two channels, which can be used as a systematic reference to facilitate further research in this area.

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

The Dawn Framing Camera (FC) has imaged the northern hemisphere of the Asteroid (4) Vesta at high spatial resolution and coverage. This study represents the first investigation of the overall geology of the northern hemisphere (22–90°N, quadrangles Av-1, 2, 3, 4 and 5) using these unique Dawn mission observations. We have compiled a morphologic map and performed crater size–frequency distribution (CSFD) measurements to date the geologic units. The hemisphere is characterized by a heavily cratered surface with a few highly subdued basins up to ∼200 km in diameter. The most widespread unit is a plateau (cratered highland unit), similar to, although of lower elevation than the equatorial Vestalia Terra plateau. Large-scale troughs and ridges have regionally affected the surface. Between ∼180°E and ∼270°E, these tectonic features are well developed and related to the south pole Veneneia impact (Saturnalia Fossae trough unit), elsewhere on the hemisphere they are rare and subdued (Saturnalia Fossae cratered unit). In these pre-Rheasilvia units we observed an unexpectedly high frequency of impact craters up to ∼10 km in diameter, whose formation could in part be related to the Rheasilvia basin-forming event. The Rheasilvia impact has potentially affected the northern hemisphere also with S–N small-scale lineations, but without covering it with an ejecta blanket. Post-Rheasilvia impact craters are small (<60 km in diameter) and show a wide range of degradation states due to impact gardening and mass wasting processes. Where fresh, they display an ejecta blanket, bright rays and slope movements on walls. In places, crater rims have dark material ejecta and some crater floors are covered by ponded material interpreted as impact melt.

Oppia Quadrangle Av-10 (288–360°E, ±22°) is a junction of key geologic features that preserve a rough history of Asteroid (4) Vesta and serves as a case study of using geologic mapping to define a relative geologic timescale. Clear filter images, stereo-derived topography, slope maps, and multispectral color-ratio images from the Framing Camera on NASA’s Dawn spacecraft served as basemaps to create a geologic map and investigate the spatial and temporal relationships of the local stratigraphy. Geologic mapping reveals the oldest map unit within Av-10 is the cratered highlands terrain which possibly represents original crustal material on Vesta that was then excavated by one or more impacts to form the basin Feralia Planitia. Saturnalia Fossae and Divalia Fossae ridge and trough terrains intersect the wall of Feralia Planitia indicating that this impact basin is older than both the Veneneia and Rheasilvia impact structures, representing Pre-Veneneian crustal material. Two of the youngest geologic features in Av-10 are Lepida (∼45 km diameter) and Oppia (∼40 km diameter) impact craters that formed on the northern and southern wall of Feralia Planitia and each cross-cuts a trough terrain. The ejecta blanket of Oppia is mapped as ‘dark mantle’ material because it appears dark orange in the Framing Camera ‘Clementine-type’ color-ratio image and has a diffuse, gradational contact distributed to the south across the rim of Rheasilvia. Mapping of surface material that appears light orange in color in the Framing Camera ‘Clementine-type’ color-ratio image as ‘light mantle material’ supports previous interpretations of an impact ejecta origin. Some light mantle deposits are easily traced to nearby source craters, but other deposits may represent distal ejecta deposits (emplaced >5 crater radii away) in a microgravity environment.

The Quadrangles Av-11 and Av-12 on Vesta are located at the northern rim of the giant Rheasilvia south polar impact basin. The primary geologic units in Av-11 and Av-12 include material from the Rheasilvia impact basin formation, smooth material and different types of impact crater structures (such as bimodal craters, dark and bright crater ray material and dark ejecta material). Av-11 and Av-12 exhibit almost the full range of mass wasting features observed on Vesta, such as slump blocks, spur-and-gully morphologies and landslides within craters. Processes of collapse, slope instability and seismically triggered events force material to slump down crater walls or scarps and produce landslides or rotational slump blocks. The spur-and-gully morphology that is known to form on Mars is also observed on Vesta; however, on Vesta this morphology formed under dry conditions.

A variety of geologic landforms and features are observed within quadrangle Av-13 Tuccia in the southern hemisphere of Vesta. The quadrangle covers parts of the highland Vestalia Terra as well as the floors of the large Rheasilvia and Veneneia impact basins, which results in a substantial elevation difference of more than 40 km between the northern and the southern portions of the quadrangle. Measurements of crater size–frequency distributions within and surrounding the Rheasilvia basin indicate that gravity-driven mass wasting in the interior of the basin has been important, and that the basin has a more ancient formation age than would be expected from the crater density on the basin floor alone. Subsequent to its formation, Rheasilvia was superimposed by several mid-sized impact craters. The most prominent craters are Tuccia, Eusebia, Vibidia, Galeria, and Antonia, whose geology and formation ages are investigated in detail in this work. These impact structures provide a variety of morphologies indicating different sorts of subsequent impact-related or gravity-driven mass wasting processes. Understanding the geologic history of the relatively young craters in the Rheasilvia basin is important in order to understand the even more degraded craters in other regions of Vesta.

As part of systematic global mapping of Vesta using data returned by the Dawn spacecraft, we have produced a geologic map of the north pole quadrangle, Av-1 Albana. Extensive seasonal shadows were present in the north polar region at the time of the Dawn observations, limiting the ability to map morphological features and employ color or spectral data for determination of composition. The major recognizable units present include ancient cratered highlands and younger crater-related units (undivided ejecta, and mass-wasting material on crater floors). The antipode of Vesta’s large southern impact basins, Rheasilvia and Veneneia, lie within or near the Av-1 quadrangle. Therefore it is of particular interest to search for evidence of features of the kind that are found at basin antipodes on other planetary bodies. Albedo markings known as lunar swirls are correlated with basin antipodes and the presence of crustal magnetic anomalies on the Moon, but lighting conditions preclude recognition of such albedo features in images of the antipode of Vesta’s Rheasilvia basin. “Hilly and lineated terrain,” found at the antipodes of large basins on the Moon and Mercury, is not present at the Rheasilvia or Veneneia antipodes. We have identified small-scale linear depressions that may be related to increased fracturing in the Rheasilvia and Veneneia antipodal areas, consistent with impact-induced stresses (Buczkowski, D. et al. [2012b]. Analysis of the large scale troughs on Vesta and correlation to a model of giant impact into a differentiated asteroid. Geol. Soc. of America Annual Meeting. Abstract 152-4; Bowling, T.J. et al. [2013]. J. Geophys. Res. – Planets, 118. http://dx.doi.org/10.1002/jgre.20123). The general high elevation of much of the north polar region could, in part, be a result of uplift caused by the Rheasilvia basin-forming impact, as predicted by numerical modeling (Bowling, T.J. et al. [2013]. J. Geophys. Res. – Planets, 118. http://dx.doi.org/10.1002/jgre.20123). However, stratigraphic and crater size–frequency distribution analysis indicate that the elevated terrain predates the two southern basins and hence is likely a remnant of the ancient vestan crust. The lack of large-scale morphological features at the basin antipodes can be attributed to weakened antipodal constructive interference of seismic waves caused by an oblique impact or by Vesta’s non-spherical shape, or by attenuation of seismic waves because of the physical properties of Vesta’s interior. A first-order analysis of the Dawn global digital elevation model for Vesta indicates that areas of permanent shadow are unlikely to be present in the vicinity of the north pole.