Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

Controlling transition probability from matter-wave soliton to chaos

For a Bose-Einstein condensate loaded into a weak traveling optical superlattice it is demonstrated that under a stochastic initial set and in a given parameter region the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically, and different chaotic regions associated with different chaos probabilities are found. The results suggest a feasible method for eliminating or strengthening chaos by modulating the moving superlattice experimentally.Comment: 4 pages, 2 figure

Discrete chaotic states of a Bose-Einstein condensate

We find the different spatial chaos in a one-dimensional attractive Bose-Einstein condensate interacting with a Gaussian-like laser barrier and perturbed by a weak optical lattice. For the low laser barrier the chaotic regions of parameters are demonstrated and the chaotic and regular states are illustrated numerically. In the high barrier case, the bounded perturbed solutions which describe a set of discrete chaotic states are constructed for the discrete barrier heights and magic numbers of condensed atoms. The chaotic density profiles are exhibited numerically for the lowest quantum number, and the analytically bounded but numerically unbounded Gaussian-like configurations are confirmed. It is shown that the chaotic wave packets can be controlled experimentally by adjusting the laser barrier potential.Comment: 7 pages, 5 figure

Business Ecosystem and Stakeholders’ Role Transformation: Evidence from China’s Emerging Electric Vehicle Industry

Nurturing an emerging industry’s business ecosystem always requires stakeholders’ efforts and role transformation. By systematically reviewing and studying the evolution of the Chinese electric vehicle industry, this paper constructs a three-dimensional theoretical framework including stages of business ecosystem lifecycle, stakeholder classification and functional roles, to analyse the transformation both of different stakeholders and their functional roles. The findings show that business ecosystem stakeholders have experienced role transformation following a mechanism defined as the ‘Triple Oscillation’ Model during the evolution of the emerging industry. These findings also help develop a conceptual model of agent-based system for business ecosystem evolution, which could be a starting point for further emerging industry study

Magnetic Field Effect on the Phase Transition in AdS Soliton Spacetime

We investigate the scalar perturbations in an AdS soliton background coupled to a Maxwell field via marginally stable modes. In the probe limit, we study the magnetic field effect on the holographic insulator/superconductor phase transition numerically and analytically. The condensate will be localized in a finite circular region for any finite constant magnetic field. Near the critical point, we find that there exists a simple relation among the critical chemical potential, magnetic field, the charge and mass of the scalar field. This relation indicates that the presence of the magnetic field causes the phase transition hard.Comment: 15 pages, 3 figures, 2 tables. contents improved and references adde

Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.Comment: 11 pages, 4 figure

High Dimensional Apollonian Networks

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension

STM observation of electronic wave interference effect in finite-sized graphite with dislocation-network structures

Superperiodic patterns near a step edge were observed by STM on several-layer-thick graphite sheets on a highly oriented pyrolitic graphite substrate, where a dislocation network is generated at the interface between the graphite overlayer and the substrate. Triangular- and rhombic-shaped periodic patterns whose periodicities are around 100 nm were observed on the upper terrace near the step edge. In contrast, only outlines of the patterns similar to those on the upper terrace were observed on the lower terrace. On the upper terrace, their geometrical patterns gradually disappeared and became similar to those on the lower terrace without any changes of their periodicity in increasing a bias voltage. By assuming a periodic scattering potential at the interface due to dislocations, the varying corrugation amplitudes of the patterns can be understood as changes in LDOS as a result of the beat of perturbed and unperturbed waves, i.e. the interference in an overlayer. The observed changes in the image depending on an overlayer height and a bias voltage can be explained by the electronic wave interference in the ultra-thin overlayer distorted under the influence of dislocation-network structures.Comment: 8 pages; 6 figures; Paper which a part of cond-mat/0311068 is disscussed in detai