Quantizing Strings in de Sitter Space

We quantize a string in the de Sitter background, and we find that the mass spectrum is modified by a term which is quadratic in oscillating numbers, and also proportional to the square of the Hubble constant.Comment: 13 pages. Version published in JHE

On the All-Speed Roe-type Scheme for Large Eddy Simulation of Homogeneous Decaying Turbulence

As the representative of the shock-capturing scheme, the Roe scheme fails to LES because important turbulent characteristics cannot be reproduced such as the famous k-5/3 spectral law owing to large numerical dissipation. In this paper, the Roe scheme is divided into five parts: , , , , and , which means basic upwind dissipation, pressure-difference-driven and velocity-difference-driven modification of the interface fluxes and pressure, respectively. Then, the role of each part on LES is investigated by homogeneous decaying turbulence. The results show that the parts , , and have little effect on LES. It is important especially for because it is necessary for computation stability. The large numerical dissipation is due to and , and each of them has much larger dissipation than SGS dissipation. According to these understanding, an improved all-speed LES-Roe scheme is proposed, which can give enough good LES results for even coarse grid resolution with usually adopted reconstruction

On plurisubharmonicity of the solution of the Fefferman equation and its applications to estimate the bottom of the spectrum of Laplace-Beltrami operators

In this paper, we introduce a concept of super-pseudoconvex domain. We prove that the solution of the Feffereman equation on a smoothly bounded strictly pseudoconvex domain $D$ in \CC^n is plurisubharmonic if and only if $D$ is super-pseudoconvex. As an application, we give a lower bound estimate the bottom of the spectrum of Laplace-Beltrami operators when $D$ is super-pseudoconvex by using the result of Li and Wang \cite{LiWang}

Quantum synchronization and quantum state sharing in irregular complex network

We investigate quantum synchronization phenomenon within the complex network constituted by coupled optomechanical systems and prove the unknown identical quantum states can be shared or distributed in the quantum network even though the topology is varying. Considering a channel constructed by quantum correlation, we show that quantum synchronization can sustain and maintain high levels in Markovian dissipation for a long time. We analyze state sharing process between two typical complex networks, that is, a small-world network corresponding to linear motif state sharing and a scale-free network corresponding to whole network sharing, respectively. Our results predict that linked nodes can be directly synchronized in small-world network, but the whole network will be synchronized only if some specific synchronization conditions are satisfied. Furthermore, we give the synchronization conditions analytically through analyzing network dynamics. This proposal paves the way for studying multi-interaction synchronization and achieving an effective quantum information processing in complex network

Criterion of quantum synchronization and controllable quantum synchronization based on an optomechanical system

We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the quantum synchronization effects between optomechanical systems and find that the error between the systems and the fluctuation of error are sensitive to coupling intensity by calculating the largest Lyapunov exponent of the model and quantum fluctuation, respectively. Through taking the appropriate coupling intensity, we can control quantum synchronization even under different logical relationship between switches. Finally, we simulate the dynamical evolution of the system to verify the quantum synchronization criterion and to show the ability of synchronization control

The asymptotic value of graph energy for random graphs with degree-based weights

In this paper, we investigate the energy of a weighted random graph $G_p(f)$ in $G_{n,p}(f)$, in which each edge $ij$ takes the weight $f(d_i,d_j)$, where $d_v$ is a random variable, the degree of vertex $v$ in the random graph $G_p$ of the Erd\"{o}s--R\'{e}nyi random graph model $G_{n,p}$, and $f$ is a symmetric real function on two variables. Suppose $|f(d_i,d_j)|\leq C n^m$ for some constants $C, m>0$, and $f((1+o(1))np,(1+o(1))np)=(1+o(1))f(np,np)$. Then, for almost all graphs $G_p(f)$ in $G_{n,p}(f)$, the energy of $G_p(f)$ is $(1+o(1))f(np,np)\frac{8}{3\pi}\sqrt{p(1-p)}\cdot n^{3/2},$ where $p\in(0,1)$ is any fixed and independent of $n$. Consequently, with this one basket we can get the asymptotic values of various kinds of graph energies of chemical use, such as Randi\'c energy, ABC energy, and energies of random matrices obtained from various kinds of degree-based chemical indices.Comment: 13 page

Asymmetrical interaction induced real spectra and exceptional points in a non-Hermitian Hamiltonian

Non-Hermitian systems with parity-time symmetry have been developed rapidly and hold great promise for future applications. Unlike most existing works considering the symmetry of the free energy terms (e.g., gain-loss system), in this paper, we report that a realizable non-Hermitian interaction between two quantum resonances can also have a real spectrum after the exceptional point. That phenomenon is similar with that in the gain-loss system so that the non-Hermitian interaction can be an excellent substitute for quantum gain. Such a non-Hermitian interaction can be realized in designed optomechanics, and we find that its dynamics are in accordance with those of normal gain system as expected. As examples, the phase transition near the exceptional point and the induced chaos in weak nonlinear coupling are shown and analyzed for an intuitive visual. Our results provide a platform for realizing parity-time symmetry devices and studying properties of non-Hermitian quantum mechanics

Sparse Recovery with Coherent Tight Frames via Analysis Dantzig Selector and Analysis LASSO

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly constrained $l_1$-analysis, called analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a tight frame provided that the measurement matrix satisfies a restricted isometry property adapted to the tight frame. As a special case, we consider the Gaussian noise. Further, under a sparsity scenario, with high probability, the recovery error from noisy data is within a log-like factor of the minimax risk over the class of vectors which are at most $s$ sparse in terms of the tight frame. Similar results for the analysis LASSO are showed. The above two algorithms provide guarantees only for noise that is bounded or bounded with high probability (for example, Gaussian noise). However, when the underlying measurements are corrupted by sparse noise, these algorithms perform suboptimally. We demonstrate robust methods for reconstructing signals that are nearly sparse in terms of a tight frame in the presence of bounded noise combined with sparse noise. The analysis in this paper is based on the restricted isometry property adapted to a tight frame, which is a natural extension to the standard restricted isometry property.Comment: 21 pages; Corrected some typos and grammatical error

Multi-fold Darboux transformations of the extended bigraded Toda hierarchy

With the extended logarithmic flow equations and some extended Vertex operators in generalized Hirota bilinear equations, extended bigraded Toda hierarchy(EBTH) was proved to govern the Gromov-Witten theory of orbiford $c_{NM}$ in literature. The generating function of these Gromov-Witten invariants is one special solution of the EBTH. In this paper, the multi-fold Darboux transformations and their determinant representations of the EBTH are given with two different gauge transformation operators. The two Darboux transformations in different directions are used to generate new solutions from known solutions which include soliton solutions of $(N,N)$-EBTH, i.e. the EBTH when $N=M$. From the generation of new solutions, one can find the big difference between the EBTH and the extended Toda hierarchy(ETH). Meanwhile we plotted the soliton graphs of the $(N,N)$-EBTH from which some approximation analysis will be given. From the analysis on velocities of soliton solutions, the difference between the extended flows and other flows are shown. The two different Darboux transformations constructed by us might be useful in Gromov-Witten theory of orbiford $c_{NM}$.Comment: 26 pages, accepted by Zeitschrift f\"ur Naturforschung

Restricted qq-Isometry Properties Adapted to Frames for Nonconvex lql_q-Analysis

This paper discusses reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the $l_q$-analysis optimization with $0<q\leq 1$. We first introduce a notion of restricted $q$-isometry property ($q$-RIP) adapted to a dictionary, which is a natural extension of the standard $q$-RIP, and establish a generalized $q$-RIP condition for approximate reconstruction of signals via the $l_q$-analysis optimization. We then determine how many random, Gaussian measurements are needed for the condition to hold with high probability. The resulting sufficient condition is met by fewer measurements for smaller $q$ than when $q=1$. The introduced generalized $q$-RIP is also useful in compressed data separation. In compressed data separation, one considers the problem of reconstruction of signals' distinct subcomponents, which are (approximately) sparse in morphologically different dictionaries, from few measurements. With the notion of generalized $q$-RIP, we show that under an usual assumption that the dictionaries satisfy a mutual coherence condition, the $l_q$ split analysis with $0<q\leq1$ can approximately reconstruct the distinct components from fewer random Gaussian measurements with small $q$ than when $q=1$Comment: 40 pages, 1 figure, under revision for a journa