This article reviews recent progresses in ultracold quantum gases, and it includes three subjects which are the Fermi gases across a Feshbach resonance, quantum gases in the optical lattices and the fast rotating quantum gases. In this article, we discuss many basic physics pictures and concepts in quantum gases, for examples, the resonant interaction, universality and condensation in the lowest Landau level; we introduce fundamental theoretical tools for studying these systems, such as mean-field theory for BEC-BCS crossover and for the boson Hubbard model; also, we emphasize the important unsolved problems in the forefront of this field, for instance, the temperature effect in optical lattices.

We give a brief review on the quantum information processing in decoherence-free subspace (DFS). We show how to realize the initialization of the entangled quantum states, information transfer and teleportation of quantum states, two-qubit Grover search and how to construct the quantum network in DFS, within the cavity QED regime based on a cavity-assisted interaction by single-photon pulses.

We present a quantum information network in which quantum information density is used for performing quantum computing or teleportation. The photons are entangled in quantum channels and play a role of flying ebit to transmit interaction among the nodes. A particular quantum Gaussian channel is constructed; it permits photon-encoded information to transmit quantum signals with certain quantum parallelism. The corresponding quantum dynamical mutual information is discussed, and the controlling nodes connectivity by driving the network is studied. With regard to different driving functions, the connectivity distribution of the network is complicated. They obey positive or negative power law, and also influence the assortativity coefficient or the dynamical property of the network.

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on G may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.

Considering the back-reaction of emitting particles to the black hole, a “new” horizon is suggested where thermodynamics can be built in the dynamical black hole. It, at least, means that the thermodynamics of a dynamical black hole should not be constructed at the original event horizon any more. The temperature, “new” horizon position and radiating particles’ energy will be consistent again under the theory of equilibrium thermodynamical system.

We study dynamical behaviors in coupled nonlinear oscillators and find that under certain conditions, a whole coupled oscillator system can cease oscillation and transfer to a globally nonuniform stationary state [i.e., the so-called oscillation death (OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly different from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into homogeneously steady state of a fixed point, which already exists but is unstable in the absence of coupling. For larger systems, very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features with the classical Turing pattern.

The 3-D quadratic diffeomorphism is defined as a map with a constant Jacobian. A few such examples are well known. In this paper, all possible forms of the 3-D quadratic diffeomorphisms are determined. Some numerical results are also given and discussed.

Based on the nonlinear oscillation of an airfilled bubble in weakly compressible media at prestressed state, the effective medium method is used to study the nonlinear property of the slightly compressible media permeated with air bubbles. It is this nonlinear oscillation of air bubbles that results in the nonlinear property of the porous media. Numerical results have confirmed that the nonlinearity of the porous media is usually high, though the optimal porosity is very small. Moreover, the nonlinear property is greatly affected by the prestressed state, porosity, and shear modulus of the matrix media.

In this review, we discuss some interesting issues in charm physics, which is full of puzzles and challenges. So far in this field, there exist many problems which have not obtained satisfactory answers yet as more unexpected phenomena Continue to be observed at the current facilities of high energy physics. Charm physics may become an ideal place for searching new resonances and studying non-perturbative QCD effects, moreover it is probably an area for exploring new physics beyond the Standard Model. More data will be available at the BESIII, B-factories, LHC and even the future ILC, which may open a wide window to a better understanding of its nature.