A Total Measure of Multi-Particle Quantum Correlations in Atomic Schrödinger Cat States

We propose a total measure of multi-particle quantum correlation in a system of N two-level atoms (N qubits). We construct a parameter that encompasses all possible quantum correlations among N two-level atoms in arbitrary symmetric pure states and define its numerical value to be the total measure of the net atom-atom correlations. We use that parameter to quantify the total quantum correlations in atomic Schrödinger cat states, which are generated by the dispersive interaction in a cavity. We study the variation of the net amount of quantum correlation as we vary the number of atoms from N=2 to N=100 and obtain some interesting results. We also study the variation of the net correlation, for fixed interaction time, as we increase the number of atoms in the excited state of the initial system, and notice some interesting features. We also observe the behaviour of the net quantum correlation as we continuously increase the interaction time, for the general state of N two-level atoms in a dispersive cavity.     

Conformal Operators on Forms and Detour Complexes on Einstein Manifolds

For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian signature); the cohomology spaces of these; conformally stable form spaces that we may view as spaces of conformal harmonics; operators that generalise Branson’s Q-curvature; global pairings between differential form bundles that descend to cohomology pairings. Here we show that these operators, spaces, and the theory underlying them, simplify significantly on conformally Einstein manifolds. We give explicit formulae for all the operators concerned. The null spaces for these, the conformal harmonics, and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form Laplacian. For the case of non-Ricci flat spaces this applies in all signatures and without topological restrictions. In the case of Riemannian signature and compact manifolds, this leads to new results on the global invariant pairings, including for the integral of Q-curvature against the null space of the dimensional order conformal Laplacian of Graham et al.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Comparison of shear banding in BMGs due to thermal-softening and free volume creation

This paper reports a comparative study of shear banding in BMGs resulting from thermal softening and free volume creation. Firstly, the effects of thermal softening and free volume creation on shear instability are discussed. It is known that thermal softening governs thermal shear banding, hence it is essentially energy related. However, compound free volume creation is the key factor to the other instability, though void-induced softening seems to be the counterpart of thermal softening. So, the driving force for shear instability owing to free volume creation is very different from the thermally assisted one. In particular, long wave perturbations are always unstable owing to compound free volume creation. Therefore, the shear instability resulting from coupled compound free volume creation and thermal softening may start more like that due to free volume creation. Also, the compound free volume creation implies a specific and intrinsic characteristic growth time of shear instability. Finally, the mature shear band width is governed by the corresponding diffusions (thermal or void diffusion) within the band. As a rough guide, the dimensionless numbers: Thermal softening related number B, Deborah number (denoting the relation of instability growth rate owing to compound free volume and loading time) and Lewis number (denoting the competition of different diffusions) show us their relative importance of thermal softening and free volume creation in shear banding. All these results are of particular significance in understanding the mechanism of shear banding in bulk metallic glasses (BMGs). Supported by the Chinese Academy of Sciences under the project “Multi-Scale Complex System” (Grant No. KJCX-SW-L08), the National Natural Science Foundation of China (Grant Nos. 10725211 and 10721202), and the Doctorial Start-up Fund of Hunan University of Science and Technology (Grant No. E50840)     

A Confined <Emphasis Type="Italic">N</Emphasis>-Dimensional Harmonic Oscillator

We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.     

Effect of microstructure on the coercivity of HDDR Nd-Fe-B permanent magnetic alloy

The effect of the grain boundary microstructure on the anisotropy and coercivity was investigated in an HDDR Nd-Fe-B permanent magnetic alloy. Considering the special microstructure of its magnetic powder grain, an anisotropic theoretical model influenced simultaneously by the structure defect at the grain boundary and the exchange coupling interaction was put forward. The variations of the structure defect factors based on the nucleation and pinning mechanism with 2r ₀/lex (where r ₀ and lex are the defect thickness and the length of exchange coupling, respectively) were calculated. The results show that the coercivity mechanism of an HDDR Nd-Fe-B permanent magnetic alloy is greatly related to its microstructure defect at the grain boundary. For a fixed lex, when 2r ₀/lex < 1.67, the coercivity is controlled by the pinning mechanism; when 2r ₀/lex > 1.67, it is determined by the nucleation mechanism. The coercivity reaches the maximum when 2r ₀/lex = 1.67. The calculation result is consistent well with the experimental result given by Morimoto et al. Supported by the National Natural Science Foundation of China (Grant No. 50671055)     

Properties of proton-rich nuclei in a three-body model

Using a three-body model and realistic two-body potentials, we investigate the properties of the nuclei ¹⁸Ne and ²⁸S near the proton dripline. We figure out the two-proton separation energies, occupation of the valence protons, root-mean-square radii of matter and the valence protons. Besides, the spatial correlation densities are displayed to reflect the correlation between the two valence protons. The first excited 0⁺ state of ¹⁸Ne is most likely to be a halo state according to our calculation. Turning off the Coulomb interactions among the three-body systems, we get the two-neutron separation energies and configuration of the valence neutrons of their corresponding mirror nuclei. The results indicate that the three-body model is proper to describe some proton-rich nuclei and can be used to deduce reliable information.     

A version of Stöber synthesis enabling the facile prediction of silica nanospheres size for the fabrication of opal photonic crystals

A sol-gel synthesis procedure based on the method proposed by Stöber et al. (J Colloid Interface Sci 26:302–315, 1968) has been adopted for the one-step preparation of mono-dispersed silica nanospheres. An excellent control of the particle diameter over a wide range is obtained by varying the amount of silicon alkoxide only, while the concentration of all other components is kept fixed: this allows the fabrication of artificial opals with a finely tuned and precisely predictable lattice parameter.