Analysis of Unbalanced Black Ring Solutions within the Quasilocal Formalism

We investigate the properties of rotating asymptotically flat black ring solutions in five-dimensional Einstein-Maxwell-dilaton gravity with the Kaluza-Klein coupling. Within the quasilocal formalism, the balance condition for these solutions is derived by using the conservation of the renormalized boundary stress-energy tensor, which is a new method proposed by Dumitru Astefanesei and his collaborators. We also study the thermodynamics of unbalanced black rings. The conserved charges and the thermodynamical quantities are computed. Due to the existence of a conical singularity in the boundary, these quantities differ from the original regular ones. It is shown that the Smarr relation and the quantum statistical relation are still satisfied. However, we get an extra term in the first law of thermodynamics. As the balance condition is imposed this extra term vanishes.Comment: 10 page

Delivery-Secrecy Tradeoff for Cache-Enabled Stochastic Networks: Content Placement Optimization

Wireless caching has been widely recognized as a promising technique for efficient content delivery. In this paper, by taking different file secrecy levels into consideration, physical-layer security oriented content placement is optimized in a stochastic cache-enabled cellular network. We propose an analytical framework to investigate the nontrivial file delivery-secrecy tradeoff. Specifically, we first derive the closed-form expressions for the file hit and secrecy probabilities. The global optimal probabilistic content placement policy is then analytically derived in terms of hit probability maximization under file secrecy constraints. Numerical results are demonstrated to verify our analytical findings and show that the targeted file secrecy levels are crucial in balancing the file delivery-secrecy tradeoff.Comment: 5 pages, 4 figures, accepted to be published in IEEE Transactions on Vehicular Technolog

Adiabatic Conditions and the Uncertainty Relation

The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning and the reason why it is necessary from the physical point of view. In this work, we relate the adiabatic theorem to the uncertainty relation, and present a clear physical picture of the traditional quantitative condition. It is shown that the quantitative condition is just the amplitude of the probability of transition between two levels in the time interval which is of the order of the time uncertainty of the system. We also present a new sufficient condition with clear physical picture.Comment: 5 page

Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices

The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph. A universal allometric scaling law is uncovered in the minimal spanning trees, whose scaling exponent is independent of the stock market and the length of the stock index. In contrast, the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors. There are marked discrepancies in the allometric scaling behaviors between the stock indices and the Brownian motions. Using surrogate time series, we find that these discrepancies are caused by the fat-tailedness of the return distribution, the nonlinear long-term correlation, and a coupling effect between these two influence factors.Comment: 7 pages including 5 figure

Anisotropic deformation of Rydberg blockade sphere in few-atom systems

Rydberg blockade sphere persists an intriguing picture by which a number of collective many-body effects caused by the strong Rydberg-Rydberg interactions can be clearly understood and profoundly investigated. In the present work, we develop a new definition for the effective two-atom blockade radius and show that the original spherically shaped blockade surface would be deformed when the real number of atoms increases from two to three. This deformation of blockade sphere reveals spatially anisotropic and shrunken properties which strongly depend on the interatomic distance. In addition, we also study the optimal conditions for the Rydberg antiblockade effect and make predictions for improving the antiblockade efficiency in few-atom systems.Comment: 7 pages, 3 figures, submitted to Physical Review

Variable separation approach for a differential-difference system: special Toda equation

A multi-linear variable separation approach is developed to solve a differential-difference Toda equation. The semi-discrete form of the continuous universal formula is found for a suitable potential of the differential-difference Toda system. Abundant semi-discrete localized coherent structures of the potential can be found by appropriately selecting the arbitrary functions of the semi-discrete form of the universal formula.Comment: 12 pages, 6 figure

Nonlocal symmetries for bilinear equations and their applications

In this paper, nonlocal symmetries for the bilinear KP and bilinear BKP equations are re-studied. Two arbitrary parameters are introduced in these nonlocal symmetries by considering gauge invariance of the bilinear KP and bilinear BKP equations under the transformation $f\longrightarrow fe^{ax+by+ct}$. By expanding these nonlocal symmetries in powers of each of two parameters, we have derived two types of bilinear NKP hierarchies and two types of bilinear NBKP hierarchies. An impressive observation is that bilinear positive and negative KP and BKP hierarchies may be derived from the same nonlocal symmetries for the KP and BKP equations. Besides, as two concrete examples, we have deived bilinear B\"acklund transformations for $t_{-2}$-flow of the NKP hierarchy and $t_{-1}$-flow of the NBKP hierarchy. All these results have made it clear that more nice integrable properties would be found for these obtained NKP hierarchies and NBKP hierarchies. Since KP and BKP hierarchies have played an essential role in soliton theory, we believe that the bilinear NKP and NBKP hierarchies will have their right place in this field.Comment: 13 pages, 0 figure

A Correlation Analysis Method for Power Systems Based on Random Matrix Theory

The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems; in this situation, the modelbased methods need be revisited. A data-driven method, as the novel alternative, on the other hand, is proposed in this paper: it reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix, as the data source, is the key trick for this method; it is formulated by two parts: 1) status data as the basic part, and 2) factor data as the augmented part. The random matrix theory (RMT) is applied as the mathematical framework. The linear eigenvalue statistics (LESs), such as the mean spectral radius (MSR), are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach, without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study, based on the standard IEEE 118-bus system, validates the proposed method.Comment: 9 pages, 9 figures, Accepted by IEEE Trans on Smart Gri

Energy-Efficient Transmission Design in Non-Orthogonal Multiple Access

Non-orthogonal multiple access (NOMA) is considered as a promising technology for improving the spectral efficiency (SE) in 5G. In this correspondence, we study the benefit of NOMA in enhancing energy efficiency (EE) for a multi-user downlink transmission, where the EE is defined as the ratio of the achievable sum rate of the users to the total power consumption. Our goal is to maximize the EE subject to a minimum required data rate for each user, which leads to a non-convex fractional programming problem. To solve it, we first establish the feasible range of the transmitting power that is able to support each user's data rate requirement. Then, we propose an EE-optimal power allocation strategy that maximizes the EE. Our numerical results show that NOMA has superior EE performance in comparison with conventional orthogonal multiple access (OMA)

Adiabatic and high-fidelity quantum gates with hybrid Rydberg-Rydberg interactions

Rydberg blockaded gate is a fundamental ingredient for scalable quantum computation with neutral Rydberg atoms. However the fidelity of such a gate is intrinsically limited by a blockade error coming from a Rydberg level shift that forbids its extensive use. Based on a dark-state adiabatic passage, we develop a novel protocol for realizing a two-atom blockade-error-free quantum gate in a hybrid system with simultaneous van der Waals (vdWsI) and resonant dipole-dipole interactions (DDI). The basic idea relies on converting the roles of two interactions, which is, the DDI serves as one time-dependent tunable pulse and the vdWsI acts as a negligible middle level shift as long as the adiabatic condition is preserved. We adopt an optimized super-Gaussian optical pulse with $k\pi$ ($k\gg 1$) area accompanied by a smooth tuning for the DDI, composing a circular stimulated Raman adiabatic passage, which can robustly ensure a faster operation time $\sim 80ns$ as well as a highly-efficient gate fidelity $\sim0.9996$. This theoretical protocol offers a flexible treatment for hybrid interactions in complex Rydberg systems, enabling on-demand design of new types of effective Rydberg quantum gate devices.Comment: 10 pages, 7 figure