First-order and continuous quantum phase transitions in the anisotropic quantum Rabi-Stark model

Various quantum phase transitions in the anisotropic Rabi-Stark model with both the nonlinear Stark coupling and the linear dipole coupling between a two-level system and a single-mode cavity are studied in this work. The first-order quantum phase transitions are detected by the level crossing of the ground-state and the first-excited state with the help of the pole structure of the transcendental functions derived by the Bogoliubov operators approach. As the nonlinear Stark coupling is the same as the cavity frequency, this model can be solved by mapping to an effective quantum oscillator. All energy levels close at the critical coupling in this case, indicating continuous quantum phase transitions. The critical gap exponent is independent of the anisotropy as long as the counter-rotating wave coupling is present, but essentially changed if the counter-rotating wave coupling disappears completely. It is suggested that the gapless Goldstone mode excitations could appear above a critical coupling in the present model in the rotating-wave approximation.Comment: 9 pages, 4 figure

The Weighted Sum Rate Maximization in MIMO Interference Networks: The Minimax Lagrangian Duality and Algorithm

We take a new perspective on the weighted sum-rate maximization in multiple-input multiple-output (MIMO) interference networks, by formulating an equivalent max-min problem. This seemingly trivial reformulation has significant implications: the Lagrangian duality of the equivalent max-min problem provides an elegant way to establish the sum-rate duality between an interference network and its reciprocal when such a duality exists, and more importantly, suggests a novel iterative minimax algorithm for the weighted sum-rate maximization. Moreover, the design and convergence proof of the algorithm use only general convex analysis. They apply and extend to any max-min problems with similar structure, and thus provide a general class of algorithms for such optimization problems. This paper presents a promising step and lends hope for establishing a general framework based on the minimax Lagrangian duality for characterizing the weighted sum-rate and developing efficient algorithms for general MIMO interference networks.Comment: 10 pages, 6 figures, submitted for publicatio

Early Fire Detection Using HEP and Space-time Analysis

In this article, a video base early fire alarm system is developed by monitoring the smoke in the scene. There are two major contributions in this work. First, to find the best texture feature for smoke detection, a general framework, named Histograms of Equivalent Patterns (HEP), is adopted to achieve an extensive evaluation of various kinds of texture features. Second, the \emph{Block based Inter-Frame Difference} (BIFD) and a improved version of LBP-TOP are proposed and ensembled to describe the space-time characteristics of the smoke. In order to reduce the false alarms, the Smoke History Image (SHI) is utilized to register the recent classification results of candidate smoke blocks. Experimental results using SVM show that the proposed method can achieve better accuracy and less false alarm compared with the state-of-the-art technologies.Comment: 9 pages, 13 figure

Quantum Theory for Mesoscopic Electric Circuits and Its Applications

This talk is assumed to exhibit an overview of the quantum theory for mesoscopic electric circuits and some of its further developments. In the theory the importance of the discreteness of electronic charge in mesoscopic electric circuit is addressed. The mesoscopic LC-design is quantized in accord with the charge discreteness. The uncertainty relation for electric charge and current is given. Because the stationary Schr\"odinger equation is turned to be Mathieu equation in $p$-representation, the wave function and energy spectrum is formally solved. As further applications, the persistent current is obtained by considering the mesoscopic ring as a pure L-design. The Coulomb blockade phenomenon occurs when applying the theory to the pure C-design. Concerning the time evolution of the states for mesoscopic electric circuit, we are able to study it by the method of characteristics. In order to study the dissipative effect in the circuit, we use density-matrix formulation. In this formulation, several type of ``off diagonal'' dissipations are expected to be discussed.Comment: Latex, 6 pages of two-collumn style, 0 figur

Asymptotics of signed Bernoulli convolutions scaled by multinacci numbers

We study the signed Bernoulli convolution $$\nu_\beta^{(n)}=*_{j=1}^n \left (\frac12\delta_{\beta^{-j}}-\frac12\delta_{-\beta^{-j}}\right ),\ n\ge 1$$ where $\beta>1$ satisfies $$\beta^m=\beta^{m-1}+\cdots+\beta+1$$ for some integer $m\ge 2$. When $m$ is odd, we show that the variation $|\nu_\beta^{(n)}|$ coincides the unsigned Bernoulli convolution $$\mu_\beta^{(n)}=*_{j=1}^n \left (\frac12\delta_{\beta^{-j}}+\frac12\delta_{-\beta^{-j}}\right ).$$ When $m$ is even, we obtain the exact asymptotic of the total variation $\|\nu_\beta^{(n)}\|$ as $n\rightarrow\infty$.Comment: 15 page

Persistent Spread Measurement for Big Network Data Based on Register Intersection

Persistent spread measurement is to count the number of distinct elements that persist in each network flow for predefined time periods. It has many practical applications, including detecting long-term stealthy network activities in the background of normal-user activities, such as stealthy DDoS attack, stealthy network scan, or faked network trend, which cannot be detected by traditional flow cardinality measurement. With big network data, one challenge is to measure the persistent spreads of a massive number of flows without incurring too much memory overhead as such measurement may be performed at the line speed by network processors with fast but small on-chip memory. We propose a highly compact Virtual Intersection HyperLogLog (VI-HLL) architecture for this purpose. It achieves far better memory efficiency than the best prior work of V-Bitmap, and in the meantime drastically extends the measurement range. Theoretical analysis and extensive experiments demonstrate that VI-HLL provides good measurement accuracy even in very tight memory space of less than 1 bit per flow.Comment: ACM SIGMETRICS 201

Acoustic scattering by a cylinder near a pressure release surface

This paper presents a study of acoustic scattering by a cylinder of either infinite or finite length near a flat pressure-release surface. A novel self-consistent method is developed to describe the multiple scattering interactions between the cylinder and the surface. The complete scattering amplitude for the cylinder is derived from a set of equations, and is numerically evaluated. The results show that the presence of the surface can either enhance or reduce the scattering of the cylinder, depending on the frequency, the composition of the cylinder, and the distance between the cylinder and the surface. Both air-filled and rigid cylinders are considered.Comment: 8 figure

The Twin Conjugacy Search Problem and Applications

We propose a new computational problem over the noncommutative group, called the twin conjugacy search problem. This problem is related to the conjugacy search problem and can be used for almost all of the same cryptographic constructions that are based on the conjugacy search problem. However, our new problem is at least hard as the conjugacy search problem. Moreover, the twin conjugacy search problem have many applications. One of the most important applications, we propose a trapdoor test which can replace the function of the decision oracle. We also show other applications of the problem, including: a non-interactive key exchange protocol and a key exchange protocol, a new encryption scheme which is secure against chosen ciphertext attack, with a very simple and tight security proof and short ciphertexts, under a weak assumption, in the random oracle model

Analytical solutions by squeezing to the anisotropic Rabi model in the nonperturbative deep-strong coupling regime

A novel, unexplored nonperturbative deep-strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation (GSRWA). Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones under a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which are omitted in the previous displaced state. The population dynamics confirm the validity of our approach for the npDSC strength. Our approach paves a way to the exploration of analysis in qubit-oscillator experiments for the npDSC strength by the displaced-squeezed state.Comment: 8 pages,4 figure

A characterization of arithmetic functions satisfying f(u2+kv2)=f2(u)+kf2(v)f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)

In this paper, we mainly discuss the characterization of a class of arithmetic functions $f: N \rightarrow C$ such that $f(u^{2}+kv^2)=f^{2}(u)+kf^{2}(v)$ $(k, u, v \in N)$. We obtain a characterization with given condition, propose a conjecture and show the result holds for $k \in \{2, 3, 4, 5 \}$