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

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

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

Correlations of chaotic eigenfunctions: a semiclassical analysis

We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schr\"odinger equation. The system we considered is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard.Comment: Revtex, 13 pages, 1 postscript figur

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

Generation of two-mode field squeezing through selective dynamics in cavity QED

We propose a scheme for the generation of a two-mode field squeezed state in cavity QED. It is based on two-channel Raman excitations of a beam of three-level atoms with random arrival times by two classical fields and two high-Q resonator modes. It is shown that by suitably choosing the intensities and detunings of fields the dynamical processes can be selective and two-mode squeezing between the cavity modes can be generated at steady state. This proposal does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.Comment: 4 pages,2 figure

Field-induced suppression of the pi-band superconductivity and magnetic hysteresis in the microwave surface resistance of MgB_2 at temperatures near T_c

We report on the magnetic-field-induced variations of the microwave surface resistance, R_s, in a polycrystalline MgB_2 sample, at different values of temperature. We have detected a magnetic hysteresis in R_s, which exhibits an unexpected plateau on decreasing the DC magnetic field below a certain value. In particular, at temperatures near T_c the hysteresis manifests itself only through the presence of the plateau. Although we do not quantitatively justify the anomalous shape of the magnetic hysteresis, we show that the results obtained in the reversible region of the R_s(H) curve can be quite well accounted for by supposing that, in this range of magnetic field, the pi-gap is almost suppressed by the applied field and, consequently, all the pi-band charge carriers are quasiparticles. On this hypothesis, we have calculated R_s(H) supposing that fluxons assume a conventional (single core) structure and the flux dynamics can be described in the framework of conventional models. From the fitting of the experimental results, we determine the values of H_{c2}^pi(T) at temperatures near T_c. In our opinion, the most important result of our investigation is that, at least at temperatures near T_c, the value of the applied field that separates the reversible and irreversible regions of the R_s(H) curves is just H_{c2}^pi(T); a qualitative discussion of the possible reason of this finding is given.Comment: 20 pages, 8 embedded figures, 2 Appendices, accepted for publication in Supercond. Sci. Techno

Classification of the Entangled states L\times N\times N

We presented a general classification scheme for the tripartite $L\times N\times N$ entangled system under stochastic local operation and classical communication. The whole classification procedure consists of two correlated parts: the simultaneous similarity transformation of a commuting matrix pair into a canonical form and the study of internal symmetry of parameters in the canonical form. Based on this scheme, a concrete example of entanglement classification for a $3\times N\times N$ system is given.Comment: 21 pages; published in Phys. Rev.