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

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

An entanglement measure for n-qubits

Recently, Coffman, Kundu, and Wootters introduced the residual entanglement for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61, 052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual entanglement for $n$ qubits, whose values are between 0 and 1. In this paper, we want to show that the residual entanglement for $n$ qubits is a natural measure of entanglement by demonstrating the following properties. (1). It is SL-invariant, especially LU-invariant. (2). It is an entanglement monotone. (3). It is invariant under permutations of the qubits. (4). It vanishes or is multiplicative for product states.Comment: 16 pages, no figure