The dynamics of entanglement and the phenomenon of entanglement sudden death (ESD) [1] are discussed in bipartite systems, measured by Wootters Concurrence. Our calculation shows that ESD appears whenever the system is open or closed and is dependent on the initial condition. The relation of the evolution of entanglement and energy transfer between the system and its surroundings is also studied.

The nuclear symmetry energy coefficients of finite nuclei are extracted by using the differences between the masses of isobaric nuclei. Based on the masses of more than 2400 nuclei with A = 9 − 270, we investigate the model dependence in the extraction of symmetry energy coefficient. We find that the extraction of the symmetry energy coefficients is strongly correlated with the forms of the Coulomb energy and the mass dependence of the symmetry energy coefficient adopted. The values of the extracted symmetry energy coefficients increase by about 2 MeV for heavy nuclei when the Coulomb correction term is involved. We obtain the bulk symmetry energy coefficient S 0 = 28.26 ± 1.3 MeV and the surface-to-volume ratio κ = 1.26 ± 0.25 MeV if assuming the mass dependence of symmetry energy coefficient a sym (A) = S 0 (1 − κ/A 1/3 ), and S 0 = 32.80 ± 1.7 MeV, κ = 2.82 ± 0.57 MeV when a sym (A) = S 0 (1 + κ/A 1/3 ) −1 is adopted.

The multiparticle entanglement in the Lipkin-Meshkov-Glick model has been discussed extensively in this paper. Measured by the global entanglement and its generalization, our calculation shows that the multiparticle entanglement can faithfully detect quantum phase transitions. For an antiferromagnetic case the multiparticle entanglement reaches the maximum at the transition point, whereas for ferromagnetic coupling, two different behaviors of multiparticle entanglement can be identified, dependent on the anisotropic parameter in the coupling.

The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this model. The possibility of the geometric phase or its derivatives as the universal order parameter of characterizing quantum phase transitions has been also discussed.

A relation between entanglement and criticality of spin chains is established. The entanglement we exploit is shared between auxiliary particles, which are isolated from each other, but are coupled to the same critical spin-1/2 chain. We analytically evaluate the reduced density matrix, and numerically show the entanglement of the auxiliary particles in the proximity of the critical points of the spin chain. We find that the entanglement induced by the spin-chain may reach one, and it can signal very well the critical points of the chain. A physical understanding and experimental realization with trapped ions are presented.PACS numbers: 03.65. Ud, 05.70.Jk Quantum entanglement lies at the heart of the difference between the quantum and classical multi-particle world, and can be treated as a useful resource in various tasks such as cryptography, quantum computation and teleportation [1]. Quantum phase transitions [2] are transitions between quantitatively distinct phases of quantum many-body systems, driven solely by quantum fluctuations. In the past decade, a great effort has been devoted to understand the relations between entanglement and quantum phase transitions [3,4,5,6,7,8,9]. In fact, it is natural to associate the quantum phase transition and entanglement once correlations are behind both of them. By sharing this point of view, one anticipates that entanglement induced by a quantum critical many-body system will furnish a dramatic signature of quantum critical points for the many-body system.On the other hand, we usually think of environment that surrounds quantum system as a source of decoherence. Recently researchers have started to investigate the positive effects [10,11,12,13,14,15,16,17] of environment, for example, environment assisted information processing and environment induced entanglement. These investigations pave a new way to engineer mechanisms of preventing, minimizing or using the impact of environment in quantum information processing. In those works, however, the environment was modelled as a set of independent quantum systems, i.e., correlations among particles in the environment were ignored. An interesting open question is whether the correlation among environmental particles can affect the entanglement induced in a bipartite system that couples to it.In this paper, we show how to exploit entanglement in auxiliary particles induced by a quantum critical manybody system as an essential tool to reveal quantum phenomena in the many-body quantum system. Indeed, quantum phase transitions are accompanied by a qualitative change in the nature of classical correlations, such drastic changes in the properties of ground states are often due to the collectiveness/randomness of interparticle couplings which are possibly reflected in entanglement between systems that couple to it. Here we adopt a spin-chain system described by the one-dimensional spin-1 2 XY model as the many-body system. Another pair of spin-1 2 systems that couple to the spin chain would act as the auxiliary particles. We o...