Choy Heng Lai

Controlling Complex Networks: How Much Energy Is Needed?

The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked dynamical systems.

Error function attack of chaos synchronization based encryption schemes

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor.

On the synchronization of different chaotic oscillators

Abstract The synchronization of two different chaotic oscillators is studied, based on an open-loop control – the entrainment control. We consider two types of synchronization: complete synchronization and effectively complete synchronization. The sufficient conditions that two different systems can be synchronized by this method is discussed. Furthermore, a hierarchical idea to synchronize multiple chaotic subsystems is proposed.

Exact solution for first-order synchronization transition in a generalized Kuramoto model

First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years. We here report the analytical solution of a generalized Kuramoto model, and derive a series of exact results for the first-order synchronization transition, including i) the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions, ii) the closed form of the forward transition point and the linear stability analysis for the incoherent state (for a Lorentzian frequency distribution), and iii) the closed forms for both the stable and unstable coherent states (and their stabilities) for the backward transition. Our results, together with elucidating the first-order nature of the transition, provide insights on the mechanisms at the basis of such a synchronization phenomenon.

Bifurcation behavior of the generalized Lorenz equations at large rotation numbers

The bifurcation structure and periodic orbits of the Lorenz–Stenflo equations at large rotation numbers are given. It is shown that rotation can lead to a much richer dynamical behavior than that of the original Lorenz system and can be used to control or modify the latter’s chaos behavior. Orbits with new topology arising from the merging and splitting of different periodic windows are observed. Abrupt changes in the one-dimensional map are pointed out and studied in terms of the interaction of the interior and exterior boundaries.

All Entangled Pure States Violate a Single Bell’s Inequality

We show that a single Bells inequality with two dichotomic observables for each observer, which originates from Hardys nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisins theorem is proved in its most general form from which it follows that for pure states Bells nonlocality and quantum entanglement are equivalent.

Scheme for unconventional geometric quantum computation in cavity QED

In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.

Fourier-Bessel analysis of patterns in a circular domain

This paper explores the use of the Fourier–Bessel analysis for characterizing patterns in a circular domain. A set of stable patterns is found to be well-characterized by the Fourier–Bessel functions. Most patterns are dominated by a principal Fourier–Bessel mode [n, m] which has the largest Fourier–Bessel decomposition amplitude when the control parameter R is close to a corresponding non-trivial root (ρn,m) of the Bessel function. Moreover, when the control parameter is chosen to be close to two or more roots of the Bessel function, the corresponding principal Fourier–Bessel modes compete to dominate the morphology of the patterns.

Nonadditive Quantum Error-Correcting Code

We report the first nonadditive quantum error-correcting code, namely, a ((9, 12, 3)) code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors. Taking advantage of the graph states, we construct explicitly a complete encoding-decoding circuit for the proposed nonadditive error-correcting code.

Analysis of spurious synchronization with positive conditional Lyapunov exponents in computer simulations

Abstract Synchronization of chaotic systems has been a field of great interest and potential applications. The necessary condition for synchronization is the negativity of the largest conditional Lyapunov exponent. Some researches have shown that negativity of the largest conditional Lyapunov exponent is not a sufficient condition for high-quality synchronization in the presence of small perturbations. However, it was reported that synchronization can be achieved with positive conditional Lyapunov exponents based on numerical simulations. In this paper, we first analyze the behavior of synchronization with positive conditional Lyapunov exponents in computer simulations of the synchronization of chaotic systems with various couplings, and demonstrate that synchronization is an outcome of finite precision in numerical simulations. It is shown that such a numerical artifact is quite common and easily occurs in numerical simulations, thus can be confusing and misleading. Some behavior and properties of the synchronized system with slightly positive conditional Lyapunov exponents can be understood based on the theory of on–off intermittency. We also study the effects of finite precision on numerical simulation of on–off intermittency. Special care should be taken in numerical simulations of chaotic systems in order not to mistake numerical artifacts as physical phenomena.