A remark on the Hard Lefschetz Theorem for K\"ahler orbifolds

We give a proof of the hard Lefschetz theorem for orbifolds that does not involve intersection homology. This answers a question of Fulton. We use a foliated version of the hard Lefschetz theorem due to El Kacimi

Thermal Entanglement in Ferrimagnetic Chains

A formula to evaluate the entanglement in an one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-1/2 and spin-s ferrimagnetic chain is rather robust against temperature, and the threshold temperature may be arbitrarily high when s is sufficiently large. This intriguing result answers unambiguously a fundamental question: ``can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures?"Comment: 4 pages, 3 figure

Single-photon transport in a one dimentional waveguide coupling to a hybrid atom-optomechanical system

We explore theoretically the single-photon transport in a single-mode waveguide that is coupled to a hybrid atom-optomechanical system in a strong optomechanical coupling regime. Using a full quantum real-space approach, transmission and reflection coefficients of the propagating single-photon in the waveguide are ob- tained. The influences of atom-cavity detuning and the dissipation of atom on the transport are also studied. Intriguingly, the obtained spectral features can reveal the strong light-matter interaction in this hybrid system.Comment: 7pages, 8figure

Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings

This study is concerned with the non-fragile H∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H∞ outputfeedback controller such that the closed-loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semidefinite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method

Revealing Majorana Fermion states in a superfluid of cold atoms subject to a harmonic potential

We here explore Majorana Fermion states in an s-wave superfluid of cold atoms in the presence of spin-orbital coupling and an additional harmonic potential. The superfluid boundary is induced by a harmonic trap. Two locally separated Majorana Fermion states are revealed numerically based on the self-consistent Bogoliubov-de Gennes equations. The local density of states are calculated, through which the signatures of Majorana excitations may be indicated experimentally

Operator fidelity susceptibility: an indicator of quantum criticality

We introduce the operator fidelity and propose to use its susceptibility for characterizing the sensitivity of quantum systems to perturbations. Two typical models are addressed: one is the transverse Ising model exhibiting a quantum phase transition, and the other is the one dimensional Heisenberg spin chain with next-nearest-neighbor interactions, which has the degeneracy. It is revealed that the operator fidelity susceptibility is a good indicator of quantum criticality regardless of the system degeneracy.Comment: Four pages, two figure

H∞ fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

In this paper, the finite-horizon H∞ fault estimation problem is investigated for a class of uncertain nonlinear time-varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoulli-distributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite-horizon fault estimator to achieve the specified H∞ performance. The time-varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities. Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach