ASU Scholarship Showcase

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.

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.

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩^β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.

What's a profession without a code of ethics? Being a legitimate profession almost requires drafting a code and, at least nominally, making members follow it. Codes of ethics (henceforth “codes”) exist for a number of reasons, many of which can vary widely from profession to profession - but above all they are a form of codified self-regulation. While codes can be beneficial, it argues that when we scratch below the surface, there are many problems at their root. In terms of efficacy, codes can serve as a form of ethical window dressing, rather than effective rules for behavior. But even more that, codes can degrade the meaning behind being a good person who acts ethically for the right reasons.

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.

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.

Plasmonic and metamaterial based nano/micro-structured materials enable spectrally selective resonant absorption, where the resonant bandwidth and absorption intensity can be engineered by controlling the size and geometry of nanostructures. Here, we demonstrate a simple, lithography-free approach for obtaining a resonant and dynamically tunable broadband absorber based on vanadium dioxide (VO2) phase transition. Using planar layered thin film structures, where top layer is chosen to be an ultrathin (20 nm) VO2 film, we demonstrate broadband IR light absorption tuning (from similar to 90% to similar to 30% in measured absorption) over the entire mid-wavelength infrared spectrum. Our numerical and experimental results indicate that the bandwidth of the absorption bands can be controlled by changing the dielectric spacer layer thickness. Broadband tunable absorbers can find applications in absorption filters, thermal emitters, thermophotovoltaics, and sensing.

Online communities are becoming increasingly important as platforms for large-scale human cooperation. These communities allow users seeking and sharing professional skills to solve problems collaboratively. To investigate how users cooperate to complete a large number of knowledge-producing tasks, we analyze Stack Exchange, one of the largest question and answer systems in the world. We construct attention networks to model the growth of 110 communities in the Stack Exchange system and quantify individual answering strategies using the linking dynamics on attention networks. We identify two answering strategies. Strategy A aims at performing maintenance by doing simple tasks, whereas strategy B aims at investing time in doing challenging tasks. Both strategies are important: empirical evidence shows that strategy A decreases the median waiting time for answers and strategy B increases the acceptance rate of answers. In investigating the strategic persistence of users, we find that users tends to stick on the same strategy over time in a community, but switch from one strategy to the other across communities. This finding reveals the different sets of knowledge and skills between users. A balance between the population of users taking A and B strategies that approximates 2:1, is found to be optimal to the sustainable growth of communities.