Measurability of D-concurrence.

An effective approach to quantify entanglement of any bipartite systems is D-concurrence, which is important in quantum information science. In this paper, we present a direct method for experimental determination of the D-concurrence of an arbitrary bipartite pure state. To do this, we show that measurement of the D-concurrence of bipartite pure state can be conversed into the measurement performed on some observables so called generalized Gell-Mann operators. We first introduce the concept of D-concurrence for a bipartite system. Then we explain the method of measuring this entanglement measure for the pure state. Finally, for clarify of the subject, we give an example consisting of two parties A and B with dimensions 3.

Study of encapsulated microbubble cluster based on association schemes perspective.

Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of a cluster of encapsulated microbubbles under the action of an ultrasound field are complex and highly nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. In this paper, based on Qin-Ferrara's model (Qin and Ferrara, 2010), the complete synchronization and cluster formation in targeted microbubbles network are studied. Also, association schemes as a novel approach are suggested for finding a relationship between coupled microbubbles elements which are immersed in blood or surrounding soft tissue. A significant advantage of this method is that the stability of the synchronized state (or symmetric eigenmode of mutual bubble oscillation) with respect to another state (another eigenmode) can now predict. More interestingly, we find a significant relationship between an isolated and multiple microbubbles. The results show that the problem of studying the dynamics of encapsulated microbubble cluster at synchronization state is dependent on the dynamical characteristics of isolated cases, shell thickness, density. Also, the distance between microbubbles has an important role in their synchronous modes.

Variational study of the interacting, spinless Su-Schrieffer-Heeger model.

We study the phase diagram and the total polarization distribution of the Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane-Mele-Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution 'walks across' smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as it happens when a Rice-Mele onsite potential is turned on.

Association schemes perspective of microbubble cluster in ultrasonic fields.

Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We remark that in general, the stability region of the cluster of oscillators at the synchronization state is characterized by Lyapunov exponent which can be defined based on the N-coupled map. As a detailed physical example, dynamics of microbubble cluster in an ultrasonic field are studied using coupled maps. Microbubble cluster dynamics have an indicative highly active nonlinear phenomenon, were not easy to be explained. In this paper, a cluster of microbubbles with a thin elastic shell based on the modified Keller-Herring equation in an ultrasonic field is demonstrated in the framework of the globally coupled map. On the other hand, a relation between the microbubble elements is replaced by a relation between the vertices. Based on this method, the stability region of microbubbles pulsations at complete synchronization state has been obtained analytically. In this way, distances between microbubbles as coupling strength play the crucial role. In the stability region, we thus observe that the problem of study of dynamics of N-microbubble oscillators reduce to that of a single microbubble. Therefore, the important parameters of the isolated microbubble such as applied pressure, driving frequency and the initial radius have effective behavior on the synchronization state.

Topological insulation in a ladder model with particle-hole and reflection symmetries.

A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the C and CI symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants of each Creutz model sum to give the mirror winding number, with winding numbers which are nonzero individually but equal and opposite in the topological phase, and both zero in the trivial phase. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibits two distinct topological regions, distinguished by the different types of reflection symmetries.