Hu Cheng-Zheng

Quantum Stackelberg Duopoly with Continuous Distributed Incomplete Information

A general model of the quantum Stackelberg duopoly is constructed by introducing the “minimal quantum structure into the Stackelberg duopoly with continuous distributed incomplete information, where both players only know the continuous distribution of the competitors unit cost. In this model, the cases with complete information, discrete distributed incomplete information, and continuous distributed asymmetric information are all involved. Because of different roles played by the total information uncertainty and the information asymmetry, the game exhibits some new interesting features, such as the total information uncertainty can counteract or improve the first-mover advantage according to the value of the quantum entanglement. Whats more, this general model will be helpful for the government to reduce the abuses of oligopolistic competition and to improve the economic efficiency.

Quantum Stackelberg Duopoly of Continuous Distributed Asymmetric Information

The minimal quantization structure is employed to investigate the quantum version of the Stackelberg duopoly with continuous distributed asymmetric information, i.e. the first mover has incomplete information that obeys a continuous distribution while the second mover has complete information. It is found that the effects of the positive quantum entanglement on the outcomes exhibit many interesting features due to the information asymmetry. Moreover, although the first-mover advantage is counteracted by the information asymmetry, the positive quantum entanglement still enhances the first-mover advantage and improves the first-mover tolerance of the information asymmetry beyond the classical limit.

Generalization of Eshelby's method to the anisotropic elasticity theory of dislocations in quasicrystals

The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelbys method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated.

Phonon dispersion relations and soft modes of 4 A carbon nanotubes

The phonon dispersion relations of three kinds of 4 A carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the (5,0) tube which are quite different from those reported previously. Our results suggest that the (5,0) tube remains metallic at very low temperature, instead of the metallic-semiconducting transition claimed before.

Group-theoretical method for physical property tensors of quasicrystals

In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.

Hall effect in quasicrystals

The relations between Hall effect and symmetry are discussed for all 2- and 3-dimensional quasicrystals with crystallographically forbidden symmetries. The results show that the numbers of independent components of the Hall coefficient (Ru) are one for 3-dimensional quasicrystals, two for those 2-dimensional quasicrystals whose symmetry group is non-Abelian, and three for those 2-dimensional quasicrystals whose symmetry group is Abelian, respectively. The quasicrystals with the same number of independent components have the same form of the components ofRn.

Linear and Nonlinear Optical Properties of Quasicrystals

An investigation is carried out on the linear and nonlinear optical properties of quasicrystals. The linear and nonlinear susceptibilities are determined for two- and three-dimensional quasicrystals. The results show that for optical linearity, two-dimensional quasicrystals are uniaxial, while icosahedral quasicrystals are optically isotropic. Meanwhile all quasicrystals, except those with 5, 5 m, N, Nmm (N = 8, 10, 12) symmetries, have no the first-order optical nonlinearity. The tensor scheme of the first order nonlinear susceptibility is the same for these eight exceptional kinds of quasicrystals.

Evaluation of some Fourier integrals inN-dimensional space for the theory of dislocations in quasicrystals

A method to evaluate some Fourier integrals is extended from two-dimensional (2-D) and three dimensional (3-D) spaces ton-dimensional (n-D) space, which are often used in the elasticity theory of dislocations in quasicrystals. Some key formulae have been given.

EXPRESSION OF THE ELASTIC ENERGY IN TWO-DIMENSIONAL QUASICRYSTALS

The application of group theory to elasticity in two-dimensional (2D) quasicrystals is presented. The expression of elastic energy as a function of gradients of the phonon and phason fields has been derived to quadratic order. The phonon response to an external stress is isotropic, but the response of phason field is anisotropic for eightfold and twelvefold symmetries.