Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.     

On explicit free field realization of current algebras

We construct the explicit free field representations of the current algebras so(2n)_k, so(2n+1)_k and sp(2n)_k for a generic positive integer n and an arbitrary level k. The corresponding energy–momentum tensors and screening currents of the first kind are also given in terms of free fields.     

DERIVATIONS OF THE 3-LIE ALGEBRA REALIZED BY gl(n, ℂ)

This paper studies structures of the 3-Lie algebra M realized by the general linear Lie algebra gl(n, ?). We show that M has only one nonzero proper ideal. We then give explicit expressions of both derivations and inner derivations of M. Finally, we investigate substructures of the (inner) derivation algebra of M.     

Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller

In this Letter, a novel method is developed for generating grid multi-scroll chaotic attractors using switching piecewise linear controller. First, a third-order linear system is designed to ensure that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions. Then, by three different types of switching control strategies, the equilibrium point can be extended along both xy plane and z axis direction, so as to generate grid multi-scroll chaotic attractors. The dynamical behaviors are further analyzed. Moreover, an improved module-based circuit is designed for realizing 5×3 and 4×4 grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.     

(2 + 1)D exotic Newton-Hooke symmetry, duality and projective phase

A particle system with a (2 + 1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton-Hooke symmetry are constructed.     

Algebraic approach to the asymmetric rigid rotor

A pure algebraic treatment of the eigenvalue equation corresponding to the asymmetric top is presented. The algebraic method employs the Holstein–Primakoff bosonic realization of the angular momentum algebra. Explicit determination of the linear boson transformation coefficients of the eigenstates is carried out by means of the coherent states formalism. No reference to special functions is needed and a completely algebraic approach is achieved. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 704–709, 2000     

Combinatorial optimization for an improved transition from fluence optimization to fluence delivery in IMRT treatment planning

The intensity modulated radiation therapy (IMRT) treatment planning problem is usually divided into three smaller problems that are solved sequentially: geometry problem, intensity problem and realization problem. There are many models and algorithms that address each one of the problems in a satisfactory way. However, these problems cannot be seen separately, because strong links exist between them. While the linkage between the geometry problem and the intensity problem is straightforward, the linkage between the intensity problem and the realization problem is all but simple and will determine the quality of the treatment planning. In practice, the linkage between these problems is, most of the times, done in a rather simple way, usually by rounding. This can lead to a significant deterioration of the treatment plan quality. We propose a combinatorial optimization approach to enable an improved transition from optimized to delivery fluence maps in IMRT treatment planning. Two clinical examples of head and neck cancer cases are used, both to present numerical evidences of the resulting deterioration of plan quality if a simplistic approach is used, and also to highlight a combinatorial optimization approach as a valuable alternative when linking the intensity problem and the realization problem.     

Completely J —positive linear systems of finite order

Completely J — positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J — positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J — symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J — symmetric realizations are discussed.     

Lorenz混沌系统的分析与电路实现

利用Matlab的数值计算和Multisim的电路模型分析和实现著名的Lorenz混沌系统,观察Lorenz混沌吸引子,加深对混沌现象的认识,可将混沌理论与实验引入到大学物理实验教学项目中。