First, in graphene quantum dot systems, conductance fluctuations are investigated from the respects of Fano resonances and quantum chaos. The conventional semi-classical theory of quantum chaotic scattering used in this field depends on an invariant classical phase-space structure. I show that for systems without an invariant classical phase-space structure, the quantum pointer states can still be used to explain the conductance fluctuations. Another finding is that the chaotic geometry is demonstrated to have similar effects as the disorders in transportations.
Second, in optomechanics systems, I find rich nonlinear dynamics. Using the semi-classical Langevin equations, I demonstrate a quasi-periodic motion is favorable for the quantum entanglement between the optical mode and mechanical mode. Then I use the quantum trajectory theory to provide a new resolution for the breakdown of the classical-quantum correspondences in the chaotic regions.
Third, I investigate the analogs of the electrical band structures and effects in the non-electrical systems. In the photonic systems, I use an array of waveguides to simulate the transport of the massive relativistic particle in a non-Hermitian scenario. A new form of Zitterbewegung is discovered as well as its analytical explanation. In mechanical systems, I use springs and mass points systems to achieve a three band degenerate band structure with a new pair of spatially separated edge states in the Dice lattice. A new semi-metal phase with the intrinsic valley-Hall effect is found.
At last, I investigate the nonlinear dynamics in the spintronics systems, in which the topological insulator couples with a magnetization. Rich nonlinear dynamics are discovered in this systems, especially the multi-stability states.
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.
Novel hydride chemistries are employed to deposit light-emitting Ge1-y Snyalloys with y ≤ 0.1 by Ultra-High Vacuum Chemical Vapor Deposition (UHV-CVD) on Ge-buffered Si wafers. The properties of the resultant materials are systematically compared with similar alloys grown directly on Si wafers. The fundamental difference between the two systems is a fivefold (and higher) decrease in lattice mismatch between film and virtual substrate, allowing direct integration of bulk-like crystals with planar surfaces and relatively low dislocation densities. For y ≤ 0.06, the CVD precursors used were digermane Ge2H6 and deuterated stannane SnD4. For y ≥ 0.06, the Ge precursor was changed to trigermane Ge3H8, whose higher reactivity enabled the fabrication of supersaturated samples with the target film parameters. In all cases, the Ge wafers were produced using tetragermane Ge4H10 as the Ge source. The photoluminescence intensity from Ge1-y Sny /Ge films is expected to increase relative to Ge1-y Sny /Si due to the less defected interface with the virtual substrate. However, while Ge1-y Sny /Si films are largely relaxed, a significant amount of compressive strain may be present in the Ge1-y Sny /Ge case. This compressive strain can reduce the emission intensity by increasing the separation between the direct and indirect edges. In this context, it is shown here that the proposed CVD approach to Ge1-y Sny /Ge makes it possible to approach film thicknesses of about 1 μm, for which the strain is mostly relaxed and the photoluminescence intensity increases by one order of magnitude relative to Ge1-y Sny /Si films. The observed strain relaxation is shown to be consistent with predictions from strain-relaxation models first developed for the Si1-x Gex /Si system. The defect structure and atomic distributions in the films are studied in detail using advanced electron-microscopy techniques, including aberration corrected STEM imaging and EELS mapping of the average diamond–cubic lattice.
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.