In this review, we introduce some methods for detecting or measuring entanglement. Several nonlinear entanglement witnesses are presented. We derive a series of Bell inequalities whose maximally violations for any multipartite qubit states can be calculated by using our formulas. Both the nonlinear entanglement witnesses and the Bell inequalities can be operated experimentally. Thus they supply an effective way for detecting entanglement. We also introduce some experimental methods to measure the entanglement of formation, and the lower bound of the convex-roof extension of negativity.

We study dynamical behaviors of the weakly interacting Bose–Einstein condensate in the onedimensional optical lattice with an overall double-well potential by solving the time-dependent Gross–Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.

Based on the density operator’s o perator-sum representation r ecently obtained by Fan and Hu for a laser process (Opt. Commun., 2008, 281: 5571; Opt. Commun., 2009, 282: 932; Phys. Lett. B, 2008, 22: 2435), we derive the evolution law of Wigner operator, the law is concisely expressed in the normally ordered formΔ(α,α*,t)=Tπ:exp?[-2T(a?e-(κ-g)t-α*)-(ae-(k-g)t-α)] :, where g and κ are the cavity gain and the loss, respectively, and T≡ (κ-g )(κ+g-2ge^{-2(κ-g) t})^-1. When t=0,Δ(α,α,t)→1π : exp?[-2(a?-α*)-(a-α)] :, which is the initial Wigner operator. Using this formalism the evolution law of Wigner functions in laser process can be directly obtained.

In reviewing some recent work in metamaterials, we highlight two exciting new frontiers just emerging in this field–metamaterials made by new electronic materials (particularly graphene) and inhomogeneous metasurfaces to control light wave-fronts.

Cavity growth in ductile metal materials under dynamic loading is investigated via the material point method. Two typical cavity effects in the region subjected to rarefaction wave are identified: (i) part of material particles flow away from the cavity in comparison to the initial loading velocity, (ii) local regions show weaker negative or even positive pressures. Neighboring cavities interact via coalescence of isobaric contours. The growth of cavity under tension shows staged behaviors. After the initial slow stage, the volume and the dimensions in both the tensile and transverse directions show linear growth rate with time until the global tensile wave arrives at the upper free surface. It is interesting that the growth rate in the transverse direction is faster than that in the tensile direction. The volume growth rate linearly increases with the initial tensile velocity. After the global tensile wave passed the cavity, both the maximum particle velocity in the tensile direction and the maximum particle velocity in the opposite direction increase logarithmically with the initial tensile speed. The shock wave reflected back from the cavity and compression wave from the free surface induce the initial behavior of interfacial instabilities such as the Richtmyer-Meshkov instability, which is mainly responsible for the irregularity in the morphology of deformed cavity. The local temperatures and distribution of hot spots are determined by the plastic work. Compared with the dynamical process, the heat conduction is much slower.

We investigate the structural and elastic properties of hexagonal Ce₂O₃ under pressure using LDA+U scheme in the frame of density functional theory (DFT). The obtained lattice constants and bulk modulus agree well with the available experimental and other theoretical data. The pressure dependences of normalized lattice parameters a/a₀ and c/c₀, ratio c/a, and normalized primitive volume V/V₀ of Ce₂O₃ are obtained. Moreover, the pressure dependences of elastic properties and three anisotropies of elastic waves of Ce₂O₃ are investigated for the first time. We find that the negative value of C₄₄ is indicative of the structural instability of the hexagonal structure Ce₂O₃ at zero temperature and 30 GPa. Finally, the density of states (DOS) of Ce₂O₃ under pressure is investigated.

It is believed that weakly interacting massive particles (WIMPs) are candidates for dark matter (DM) in our universe which come from outer space and might interact with the standard model (SM) matter of our detectors on the earth. Many collaborations in the world are carrying out various experiments to directly detect DM particles. China Jinping underground Laboratory (CJPL) is the deepest underground laboratory in the world and provides a very promising environment for DM search. China Dark matter EXperiment (CDEX) is going to directly detect the WIMP flux with high sensitivity in the low WIMP-mass region. Both CJPL and CDEX have achieved a remarkable progress in recent three years. CDEX employs a point-contact germanium (PCGe) semi-conductor detector whose energy threshold is less than 300 eV. In this report we present the measurement results of muon flux, monitoring of radioactivity and radon concentration carried out in CJPL, as well describing the structure and performance of the 1 kg-PCGe detector in CDEX-1 and 10 kgPCGe detector array in CDEX-10 including the detectors, electronics, shielding and cooling systems. Finally we discuss the physics goals of CDEX-1, CDEX-10 and the future CDEX-1T experiments.

In the past two decades, statistical physics was brought into the field of finance, applying new methods and concepts to financial time series and developing a new interdiscipline “econophysics”. In this review, we introduce several commonly used methods for stock time series in econophysics including distribution functions, correlation functions, detrended fluctuation analysis method, detrended moving average method, and multifractal analysis. Then based on these methods, we review some statistical properties of Chinese stock markets including scaling behavior, long-term correlations, cross-correlations, leverage effects, antileverage effects, and multifractality. Last, based on an agent-based model, we develop a new option pricing model — financial market model that shows a good agreement with the prices using real Shanghai Index data. This review is helpful for people to understand and research statistical physics of financial markets.

A hierarchical cluster-tendency (HCT) method in analyzing the group structure of networks of the global foreign exchange (FX) market is proposed by combining the advantages of both the minimal spanning tree (MST) and the hierarchical tree (HT). Fifty currencies of the top 50 World GDP in 2010 according to World Bank’s database are chosen as the underlying system. By using the HCT method, all nodes in the FX market network can be “colored” and distinguished. We reveal that the FX networks can be divided into two groups, iffe., the Asia-Pacific group and the Pan-European group. The results given by the hierarchical cluster-tendency method agree well with the formerly observed geographical aggregation behavior in the FX market. Moreover, an oil-resource aggregation phenomenon is discovered by using our method. We find that gold could be a better numeraire for the weekly-frequency FX data.

In our recent papers, we have identified a class of phase transitions in the market-directed resourceallocation game, and found that there exists a critical point at which the phase transitions occur. The critical point is given by a certain resource ratio. Here, by performing computer simulations and theoretical analysis, we report that the critical point is robust against various kinds of human hedge behavior where the numbers of herds and contrarians can be varied widely. This means that the critical point can be independent of the total number of participants composed of normal agents, herds and contrarians, under some conditions. This finding means that the critical points we identified in this complex adaptive system (with adaptive agents) may also be an intensive quantity, similar to those revealed in traditional physical systems (with non-adaptive units).

Based on the model of the strong correlation of counterions condensed on DNA molecule, by tailoring interaction potential, interduplex spacing and correlation spacing between condensed counterions on DNA molecule and interduplex spacing fluctuation strength, toroidal configuration, rod-like configuration and two-hole configurations are possible. The size effects of counterion structure on the toroidal structure can be detected by this model. The autocorrelation function of the tangent vectors is found as an effective way to detect the structure of toroidal conformations and the generic pathway of the process of DNA condensation. The generic pathway of all of the configurations involves an initial nucleation loop, and the next part of the DNA chain is folded on the top of the initial nucleation loop with different manners, in agreement with the recent experimental results.