The bidirectional selection between two classes widely emerges in various social lives, such as commercial trading and mate choosing. Until now, the discussions on bidirectional selection in structured human society are quite limited. We demonstrated
theoretically that the rate of successfully matching is affected greatly by individuals neighborhoods in social networks, regardless of the type of networks. Furthermore, it is found that the high average degree of networks contributes to increasing rates of successful matches. The matching performance in different types of networks has been quantitatively investigated, revealing that the small-world networks reinforces the matching rate more than scale-free networks at given average degree. In addition, our analysis is consistent with the modeling result, which provides the theoretical understanding of underlying mechanisms of matching in complex networks.
The solutions for the helical edge states for an effective continuum model for the quantum spin Hall effect in HgTe/CdTe quantum wells are presented. For a sample of a large size, the solution gives the linear dispersion for the edge states. However,
in a finite strip geometry, the edge states at two sides will couple with each other, which leads to a finite energy gap in the spectra. The gap decays in an exponential law of the width of sample. The magnetic field dependence of the edge states illustrates the difference of the edge states from those of a conventional quantum Hall strip of two-dimensional electron gas.
We investigate the current-induced spin polarization in the two-dimensional hole gas (2DHG) with the structure inversion asymmetry. By using the perturbation theory, we re-derive the effective $k$-cubic Rashba Hamiltonian for 2DHG and the generalized
spin operators accordingly. Then based on the linear response theory we calculate the current-induced spin polarization both analytically and numerically with the disorder effect considered. We have found that, quite different from the two-dimensional electron gas, the spin polarization in 2DHG depends linearly on Fermi energy in the low doping regime, and with increasing Fermi energy, the spin polarization may be suppressed and even changes its sign. We predict a pronounced peak of the spin polarization in 2DHG once the Fermi level is somewhere between minimum points of two spin-split branches of the lowest light-hole subband. We discuss the possibility of measurements in experiments as regards the temperature and the width of quantum wells.
We propose a topological quantum phase transition for quantum states with different Berry phases in hole-doped III-V semiconductor quantum wells with bulk and structure inversion asymmetry. The Berry phase of the occupied Bloch states can be characte
ristic of topological metallic states. It is found that the adjustment of thickness of the quantum well may cause a transition of Berry phase in two-dimensional hole gas. Correspondingly, the jump of spin Hall conductivity accompanies the change of the Berry phase. This property is robust against the impurity potentials in the system. Experimental detection of this topological quantum phase transition is discussed.
