ASU Scholarship Showcase

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

Background: Continuous monitoring technologies such as accelerometers and pedometers are the gold standard for physical activity (PA) measurement. However, inconsistencies in use, analysis, and reporting limit the understanding of dose–response relationships involving PA and the ability to make comparisons across studies and population subgroups. These issues are particularly detrimental to the study of PA across different ethnicities with different PA habits. This systematic review examined the inclusion of published guidelines involving data collection, processing, and reporting among articles using accelerometers or pedometers in Hispanic or Latino populations.

Methods: English (PubMed; EbscoHost) and Spanish (SCIELO; Biblioteca Virtual en Salud) articles published between 2000 and 2013 using accelerometers or pedometers to measure PA among Hispanics or Latinos were identified through systematic literature searches. Of the 253 abstracts which were initially reviewed, 57 met eligibility criteria (44 accelerometer, 13 pedometer). Articles were coded and reviewed to evaluate compliance with recommended guidelines (N = 20), and the percentage of accelerometer and pedometer articles following each guideline were computed and reported.

Results: On average, 57.1 % of accelerometer and 62.2 % of pedometer articles reported each recommended guideline for data collection. Device manufacturer and model were reported most frequently, and provision of instructions for device wear in Spanish was reported least frequently. On average, 29.6 % of accelerometer articles reported each guideline for data processing. Definitions of an acceptable day for inclusion in analyses were reported most frequently, and definitions of an acceptable hour for inclusion in analyses were reported least frequently. On average, 18.8 % of accelerometer and 85.7 % of pedometer articles included each guideline for data reporting. Accelerometer articles most frequently included average number of valid days and least frequently included percentage of wear time.

Discussion: Inclusion of standard collection and reporting procedures in studies using continuous monitoring devices in Hispanic or Latino population is generally low.

The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.