Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence

We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed $N$-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding $N+1$ pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states.Comment: 22 pages; published in J. Phys. A: Math. Theo

Chiral expansion of the π0→γγ\pi^0\rightarrow\gamma\gamma decay width

A chiral field theory of mesons has been applied to study the contribution of the current quark masses to the $\pi^0\rightarrow\gamma\gamma$ decay width at the next leading order. $2\%$ enhancement has been predicted and there is no new parameter.Comment: 9 page

The influence of reconstruction criteria on the sensitive probes of the symmetry potential

Different criteria of constructing clusters and tracing back $\Delta$ resonances from the intermediate-energy neutron-rich HICs are discussed by employing the updated UrQMD transport model. It is found that both the phase-space and the coordinate-density criteria affect the single and the double neutron/proton ratios of free nucleons at small transverse momenta, but the influence becomes invisible at large transverse momenta. The effect of different methods of reconstructing freeze-out $\Delta$s on the $\Delta^0/\Delta^{++}$ ratio is strong in a large kinetic energy region.Comment: 8 pages, 7 fig

The gravitational field of a global monopole

We present an exact solution to the non-linear equation which describes a global monopole in the flat space. We re-examine the metric and the geodesics outside the global monopole. We will see that a global monopole produces a repulsive gravitational field outside the core in addition to a solid angular deficit. The lensing property of the global monopole and the global monopole-antimonopole annihilation mechanism are studied.Comment: 8 pages, no figure

Excitation function of nucleon and pion elliptic flow in relativistic heavy-ion collisions

Within a relativistic transport (ART) model for heavy-ion collisions, we show that the recently observed characteristic change from out-of-plane to in-plane elliptic flow of protons in mid-central Au+Au collisions as the incident energy increases is consistent with the calculated results using a stiff nuclear equation of state (K=380 MeV). We have also studied the elliptic flow of pions and the transverse momentum dependence of both the nucleon and pion elliptic flow in order to gain further insight about the collision dynamics.Comment: 8 pages, 2 figure

Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states

We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to a simple way of partitioning pure n-qubit states into inequivalent families and distinguishing degenerate families from one another under SLOCC. Moreover, the classification scheme via the ranks of coefficient matrices can be combined with other schemes to build a more refined classification scheme. To exemplify we classify the nine families of four qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further into inequivalent subfamilies via the ranks of coefficient matrices, and as a result, we find 28 genuinely entangled families and all the degenerate classes can be distinguished up to permutations of the four qubits. We also discuss the completeness of the classification of four qubits into nine families

Difficulties in probing density dependent symmetry potential with the HBT interferometry

Based on the updated UrQMD transport model, the effect of the symmetry potential energy on the two-nucleon HBT correlation is investigated with the help of the coalescence program for constructing clusters, and the CRAB analyzing program of the two-particle HBT correlation. An obvious non-linear dependence of the neutron-proton (or neutron-neutron) HBT correlation function ($C_{np,nn}$) at small relative momenta on the stiffness factor $\gamma$ of the symmetry potential energy is found: when $\gamma \lesssim 0.8$, the $C_{np,nn}$ increases rapidly with increasing $\gamma$, while it starts to saturate if $\gamma \gtrsim 0.8$. It is also found that both the symmetry potential energy at low densities and the conditions of constructing clusters at the late stage of the whole process influence the two-nucleon HBT correlation with the same power.Comment: 11 pages, 4 figure