Inequalities of Hermite-Hadamard type for extended ss-convex functions and applications to means

In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of special means.Comment: 17 page

qq-Deformed Chern Characters for Quantum Groups SUq(N)SU_{q}(N)

In this paper, we introduce an $N\times N$ matrix $\epsilon^{a\bar{b}}$ in the quantum groups $SU_{q}(N)$ to transform the conjugate representation into the standard form so that we are able to compute the explicit forms of the important quantities in the bicovariant differential calculus on $SU_{q}(N)$, such as the $q$-deformed structure constant ${\bf C}_{IJ}^{~K}$ and the $q$-deformed transposition operator $\Lambda$. From the $q$-gauge covariant condition we define the generalized $q$-deformed Killing form and the $m$-th $q$-deformed Chern class $P_{m}$ for the quantum groups $SU_{q}(N)$. Some useful relations of the generalized $q$-deformed Killing form are presented. In terms of the $q$-deformed homotopy operator we are able to compute the $q$-deformed Chern-Simons $Q_{2m-1}$ by the condition $dQ_{2m-1}=P_{m}$, Furthermore, the $q$-deformed cocycle hierarchy, the $q$-deformed gauge covariant Lagrangian, and the $q$-deformed Yang-Mills equation are derived

On the Capability of Measurement-Based Quantum Feedback

As a key method in dealing with uncertainties, feedback has been understood fairly well in classical control theory. But for quantum control systems, the capability of measurement-based feedback control (MFC) has not been investigated systematically. In contrast to the control of classical systems where the measurement effect is negligible, the quantum measurement will cause a quantum state to collapse, which will inevitably introduce additional uncertainties besides the system initial uncertainty. Therefore, there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement, and thus a theoretical investigation of the capability of MFC is of fundamental importance. In this paper, inspired by both the Heisenberg uncertainty principle for quantum systems and the investigation of the feedback capability for classical systems, we try to answer the following three basic questions: (i) How to choose the measurement channel appropriately? (ii) Is the MFC still superior to the open loop control in dealing with the system information uncertainties? and (iii) What is the maximum capability or limitation of the MFC? These questions will be answered theoretically by establishing several theorems concerning the asymptotic reachability of eigenstates of a typical class of Hamiltonian control mode.Comment: 27 page

The modified Seiberg-Witten monopole equations and their exact solutions

The modified Seiberg-Witten monopole equations are presented in this letter. These equations have analytic solutions in the whole 1+3 Minkowski space with finite energy. The physical meaning of the equations and solutions are discussed here.Comment: RevTex, 6 page, no figur

PPV modelling of memristor-based oscillator

In this letter, we propose for the first time a method of abstracting the PPV (Perturbation Projection Vector) characteristic of the up-to-date memristor-based oscillators. Inspired from biological oscillators and its characteristic named PRC (Phase Response Curve), we build a bridge between PRC and PPV. This relationship is verified rigorously using the transistor level simulation of Colpitts and ring oscillators, i.e., comparing the PPV converted from PRC and the PPV obtained from accurate PSS+PXF simulation. Then we apply this method to the PPV calculation of the memristor-based oscillator. By keeping the phase dynamics of the oscillator and dropping the details of voltage/current amplitude, the PPV modelling is highly efficient to describe the phase dynamics due to the oscillator coupling, and will be very suitable for the fast simulation of large scale oscillatory neural networks

Enhancing Hydrogen Generation Through Nanoconfinement of Sensitizers and Catalysts in a Homogeneous Supramolecular Organic Framework.

Enrichment of molecular photosensitizers and catalysts in a confined nanospace is conducive for photocatalytic reactions due to improved photoexcited electron transfer from photosensitizers to catalysts. Herein, the self-assembly of a highly stable 3D supramolecular organic framework from a rigid bipyridine-derived tetrahedral monomer and cucurbit[8]uril in water, and its efficient and simultaneous intake of both [Ru(bpy)3 ]2+ -based photosensitizers and various polyoxometalates, that can take place at very low loading, are reported. The enrichment substantially increases the apparent concentration of both photosensitizer and catalyst in the interior of the framework, which leads to a recyclable, homogeneous, visible light-driven photocatalytic system with 110-fold increase of the turnover number for the hydrogen evolution reaction

Anderson localization in the Non-Hermitian Aubry-Andr\'e-Harper model with physical gain and loss

We investigate the Anderson localization in non-Hermitian Aubry-Andr\'e-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.Comment: 6 pages, 4 figure

Generalized Aubry-Andr\'e-Harper model with p-wave superconducting pairing

We investigate a generalized Aubry-Andr\'e-Harper (AAH) model with p-wave superconducting pairing. Both the hopping amplitudes between the nearest neighboring lattice sites and the on-site potentials in this system are modulated by a cosine function with a periodicity of $1/\alpha$. In the incommensurate case [$\alpha=(\sqrt{5}-1)/2$], due to the modulations on the hopping amplitudes, the critical region of this quasiperiodic system is significantly reduced and the system becomes more easily to be turned from extended states to localized states. In the commensurate case ($\alpha = 1/2$), we find that this model shows three different phases when we tune the system parameters: Su-Schrieffer-Heeger (SSH)-like trivial, SSH-like topological, and Kitaev-like topological phases. The phase diagrams and the topological quantum numbers for these phases are presented in this work. This generalized AAH model combined with superconducting pairing provides us with a useful testfield for studying the phase transitions from extended states to Anderson localized states and the transitions between different topological phases.Comment: 9 pages, 5 figure

Quench dynamics in the Aubry-Andr\'e-Harper model with \textit{p}-wave superconductivity

The Anderson localization phase transition in the Aubry-Andr\'e-Harper (AAH) model with \textit{p}-wave superconducting (SC) pairing is numerically investigated by suddenly changing the on-site potential from zero to various finite values which fall into the extended, critical and localized phase regimes shown in this model. The time evolutions of entanglement entropy (EE), mean width of wave packets and Loschmidt echo of the system exhibit distinct but consistent dynamical signatures in those three phases. Specifically, the EE grows as a power function of time with the exponent of which varies in the extended phase but keeps almost unchanged in the critical phase for different quench parameters. However, if the system is in the localized phase after a quench, the EE grows much slower and will soon get saturated. The time-dependent width of wave packets in the system shows similar behaviors as the EE. In addition, from the perspective of dynamical phase transition, we find that the Loschmidt echo oscillates and always keeps finite when the system is quenched in the extended phase. In contrast, in the critical or localized phase, the echo will reach to zero at some time intervals or will decay almost to zero after a long-time evolution. The universal features of these quantities in the critical phase of the system with various SC pairing amplitudes are also observed.Comment: 9 pages, 6 figure

Quantum Clique Gossiping

This paper establishes a framework for the acceleration of quantum gossip algorithms by introducing local clique operations to networks of interconnected qubits. Cliques are local structures in complex networks being complete subgraphs. Based on cyclic permutations, clique gossiping leads to collective multi-party qubit interactions. This type of algorithm can be physically realized by a series of local environments using coherent methods. First of all, we show that at reduced states, these cliques have the same acceleration effects as their roles in accelerating classical gossip algorithms, which can even make possible finite-time convergence for suitable network structures. Next, for randomized selection of cliques where node updates enjoy a more self-organized and scalable sequencing, we show that the rate of convergence is precisely improved by $\mathcal{O}(k/n)$ at the reduced states, where $k$ is the size of the cliques and $n$ is the number of qubits in the network. The rate of convergence at the coherent states of the overall quantum network is proven to be decided by the spectrum of a mean-square error evolution matrix. Explicit calculation of such matrix is rather challenging, nonetheless, the effect of cliques on the coherent states' dynamics is illustrated via numerical examples. Interestingly, the use of larger quantum cliques does not necessarily increase the speed of the network density aggregation, suggesting quantum network dynamics is not entirely decided by its classical topology.Comment: 12 pages, 2 figure