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.

Background: Foam rolling has been shown to acutely increase range of motion (ROM) during knee flexion and hip flexion with the experimenter applying an external force, yet no study to date has measured hip extensibility as a result of foam rolling with controlled knee flexion and hip extension moments. The purpose of this study was to investigate the acute effects of foam rolling on hip extension, knee flexion, and rectus femoris length during the modified Thomas test.

Methods: Twenty-three healthy participants (male = 7; female = 16; age = 22 ± 3.3 years; height = 170 ± 9.18 cm; mass = 67.7 ± 14.9 kg) performed two, one-minute bouts of foam rolling applied to the anterior thigh. Hip extension and knee flexion were measured via motion capture before and after the foam rolling intervention, from which rectus femoris length was calculated.

Results: Although the increase in hip extension (change = +1.86° (+0.11, +3.61); z(22) = 2.08; p = 0.0372; Pearson’s r = 0.43 (0.02, 0.72)) was not due to chance alone, it cannot be said that the observed changes in knee flexion (change = −1.39° (−5.53, +2.75); t(22) = −0.70; p = 0.4933; Cohen’s d = − 0.15 (−0.58, 0.29)) or rectus femoris length (change = −0.005 (−0.013, +0.003); t(22) = −1.30; p = 0.2070; Cohen’s d = − 0.27 (−0.70, 0.16)) were not due to chance alone.

Conclusions: Although a small change in hip extension was observed, no changes in knee flexion or rectus femoris length were observed. From these data, it appears unlikely that foam rolling applied to the anterior thigh will improve passive hip extension and knee flexion ROM, especially if performed in combination with a dynamic stretching protocol.

Muscle hypertrophy and atrophy occur frequently as a result of mechanical loading or unloading, with implications for clinical, general, and athletic populations. The effects of muscle hypertrophy and atrophy on force production and joint moments have been previously described. However, there is a paucity of research showing how hypertrophy and atrophy may affect moment arm (MA) lengths. The purpose of this model was to describe the mathematical relationship between the anatomical cross-sectional area (ACSA) of a muscle and its MA length. In the model, the ACSAs of the biceps brachii and brachialis were altered to hypertrophy up to twice their original size and to atrophy to one-half of their original size. The change in MA length was found to be proportional to the arcsine of the square root of the change in ACSA. This change in MA length may be a small but important contributor to strength, especially in sports that require large joint moments at slow joint angular velocities, such as powerlifting. The paradoxical implications of the increase in MA are discussed, as physiological factors influencing muscle contraction velocity appear to favor a smaller MA length for high velocity movements but a larger muscle MA length for low velocity, high force movements.

Background: The purpose of this study was to compare the peak electromyography (EMG) of the most commonly-used position in the literature, the prone bent-leg (90°) hip extension against manual resistance applied to the distal thigh (PRONE), to a novel position, the standing glute squeeze (SQUEEZE).

Methods: Surface EMG electrodes were placed on the upper and lower gluteus maximus of thirteen recreationally active females (age = 28.9 years; height = 164 cm; body mass = 58.2 kg), before three maximum voluntary isometric contraction (MVIC) trials for each position were obtained in a randomized, counterbalanced fashion.

Results: No statistically significant (p < 0.05) differences were observed between PRONE (upper: 91.94%; lower: 94.52%) and SQUEEZE (upper: 92.04%; lower: 85.12%) for both the upper and lower gluteus maximus. Neither the PRONE nor SQUEEZE was more effective between all subjects.

Conclusions: In agreement with other studies, no single testing position is ideal for every participant. Therefore, it is recommended that investigators employ multiple MVIC positions, when possible, to ensure accuracy. Future research should investigate a variety of gluteus maximus MVIC positions in heterogeneous samples.

Training the bench press exercise on a traditional flat bench does not induce a level of instability as seen in sport movements and activities of daily living. Twenty participants were recruited to test two forms of instability: using one dumbbell rather than two and lifting on the COR bench compared to a flat bench. Electromyography (EMG) amplitudes of the pectoralis major, middle trapezius, external oblique, and internal oblique were recorded and compared. Differences in range of motion (ROM) were evaluated by measuring an angular representation of the shoulder complex. Four separate conditions of unilateral bench press were tested while lifting on a: flat bench with one dumbbell, flat bench with two dumbbells, COR Bench with one dumbbell, and COR Bench with two dumbbells. The results imply that there are no differences in EMG amplitude or ROM between the COR bench and traditional bench. However, greater ROM was found to be utilized in the single dumbbell condition, both in the COR bench and the flat bench.

Many strength and conditioning coaches utilize the good morning (GM) to strengthen the hamstrings and spinal erectors. However, little research exists on its electromyography (EMG) activity and kinematics, and how these variables change as a function of load. The purpose of this investigation was to examine how estimated hamstring length, integrated EMG (IEMG) activity of the hamstrings and spinal erectors, and kinematics of the lumbar spine, hip, knee, and ankle are affected by changes in load. Fifteen trained male participants (age = 24.6 ± 5.3 years; body mass = 84.7 ± 11.3 kg; height = 180.9 ± 6.8 cm) were recruited for this study. Participants performed five sets of the GM, utilizing 50, 60, 70, 80, and 90% of one-repetition maximum (1RM) in a randomized fashion. IEMG activity of hamstrings and spinal erectors tended to increase with load. Knee flexion increased with load on all trials. Estimated hamstring length decreased with load. However, lumbar flexion, hip flexion, and plantar flexion experienced no remarkable changes between trials. These data provide insight as to how changing the load of the GM affects EMG activity, kinematic variables, and estimated hamstring length. Implications for hamstring injury prevention are discussed. More research is needed for further insight as to how load affects EMG activity and kinematics of other exercises.