Quantum chaos and tunneling in the kicked top

We analyze the dynamics of the kicked top in a deeply quantum regime. Signatures of classical chaos in the quantum dynamics that can be identified from a semiclassical treatment persist in a deeply quantum regime. Structures in the classical-phase space can also be identified in the tunneling dynamics of the quantum system. Our results show that quantum chaos is observable in the regime that is accessible to future experiments with trapped ions or cold atoms.     

Classical and quantum chaos for a kicked top

We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the quantum dynamics takes place in a finite dimensional Hilbert space. We find a distinction between regular and irregular behavior for times exceeding the quantum mechanical quasiperiod at which classical behavior, whether chaotic or regular, has died out in quantum means. The degree of level repulsion depends on whether or not the top is endowed with a generalized time reversal invariance.     

Gravity waves, chaos, and spinning compact binaries

Spinning compact binaries are shown to be chaotic in the post-Newtonian expansion of the two-body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.     

Transient reemergent order in convective spatial chaos

Transient turbulent states leading to a stable convective structure have been observed in Rayleigh-Bénard convection at high Rayleigh number and in confined geometry. This turbulent state consists in alternating sequences of spatial chaos stochastically interrupted by intermittent lockings on definite convective structures.     

Field-induced transitions and spatial chaos in the classical XY spin chain

We study the lowest-lying excitation of a classical ferromagnetic XY spin chain, in the presence of a symmetry breaking magnetic field. Extremizing the energy of this system leads to a two-dimensional nonlinear map, whose allowed phase space shrinks with increasing field in a nontrivial manner. The orbits of the map represent the set of extremum energy spin configurations. For each field, we compute the energy of the members of this set and find the lowest energy among them, excluding the obvious ground state configuration with all spins parallel along the field direction. This state turns out to be the unstable fixed point of the map. We show that up to a certain (primary) critical field, a separatrixlike 2pi soliton configuration is the lowest-energy excitation, with an energy very close to the ground state energy. For any field beyond this critical field, the soliton disappears and lowest excitation is a librational configuration corresponding to the outermost orbit in the phase plot at that field. Further, its energy is found to be much higher than the ground state energy, leading to a sharp jump in the difference in energy between the former and the latter at this field. With further increase in the field, sharp jumps in the excitation energy arise at certain secondary critical fields as well. We show that these appear when the corresponding spin configurations become commensurate. This complex behavior of the energy is interpreted and its effect on the magnetization and static susceptibility of the system is also studied.     

Temporal chaos versus spatial mixing in reaction-advection-diffusion systems

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of different components, is demonstrated to work accurately for time-dependent flows and different Pe clet numbers.     

Characterization of the spatial complex behavior and transition to chaos in flow systems

We introduce a “spatial” Lyapunov exponent to characterize the complex behavior of non-chaotic but convectively unstable flow sytems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that there exists a relation between the spatial-complexity index we define and the comoving Lyapunov exponents. In such systems the transition to chaos, i.e., the occurrence of a positive Lyapunov exponent, can manifest itself in two different ways. In the first case (from neither chaotic nor spatially complex behavior to chaos) one observes the typical scenario; i.e., as the system size grows up the spectrum of the Lyapunov exponents gives rise to a density. In the second case (when the chaos develops from a convectively unstable situation) one observes only a finite number of positive Lyapunov exponents.     

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

Based on the Melnikov method, we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value, which involves the angular momentum J. Under the spatial perturbation, however, it is found that spatial chaos always occurs, independent of the perturbation amplitude.     

3-D image formation by transformation of time signals into spatial structures

A method of 3-D image formation based on the use of radiation pulse sources and focusing systems with scanning during a pulse (BSP) has been described. These systems transform time signals into quasi-interference spatial structures. The BSP resolution power exceeds considerably the Raleigh criterion and depends neither on the distance to the object nor on the focusing system size.     

Controlling chaos: Stabilization of fixed points and creation of new stable attractors in 1-D maps

In this paper we have tried to stabilize the unstable fixed points for a class of 1-D maps by using a multiplicative nonlinear feedback control mechanism. We have also used such control to create new attractors (which did not exist in the original system), to suit our requirement. The control is also found to work in the presence of noise.     

OCDMA系统中2-D码和3-D码

光码分多址(OCDMA)技术主要应用在接入网中。设计大容量的地址码是该技术实用化的前提。本文在构造2 D素数码的基础上提出了一种用于OCDMA系统的空域/频域/时域3 D地址码。这种码基于素数序列运算。理论分析和数学计算结果表明，3 D码比2 D码的容量更大，系统带宽效率更高，误码率(BER)更低，表现出的性能更好。     

基于空间二进制编码的3-D形貌测量方法

介绍了一种基于空间二进制编码的非接触3-D形貌测量方法.它用一台LCD投影仪对被测物体表面进行空间编码,再用一台CCD摄像机获取物体编码信息,最后用三角法原理从摄像机图像中获取三维形貌数据.提出了基于三角法的空间二进制码的重要特性,描述了高效编码的构造方法.用这个构造方法构造出一个完全数字化的7位字长的二进制编码.基于这种编码的3-D形貌测量方法在被测物体表面非常不连续和非构造的环境下取得了良好的测量结果.     

空间编码与灰度投影相结合实现高效3-D形貌测量的研究

介绍了一种结合空间编码与灰度投影来实现高效三维形貌测量的方法。用空间编码完成对被测空间的粗略编码,用灰度投影完成精确编码,将它们结合起来得到被测物体表面丰富的编码信息,作为一种基于三角法的三维形貌测量方法,能够在物体表面非常不连续和外部光照造成的背景光强分布不确定的情况下工作良好。同时,与传统的空间编码方法相比,它大大提高了空间编码的效率。实验表明,该方法用５ 幅图像取得了与灰度码１０幅图像相当的测量结果。     

Control of spatiotemporal chaos: dependence of the minimum pinning distance on the spatial measure entropy

We investigate the control of spatiotemporal chaos by external forcing at equidistant points (pinning sites) in one-dimensional systems. A monotonic decrease of the minimum distance between pinning sites versus the spatial measure entropy (in the absence of forcing) can be obtained for an appropriate choice of the forcing procedure. Such a relation between a feature for control and the disorder of the uncontrolled system is shown for four systems: binary cellular automata, coupled logistic equations, a stick-slip model and coupled differential equations.     

Correlation dimension of the flow and spatial development of dynamical chaos in a boundary layer

The relation between the spatial development of turbulence in a real hydrodynamical system (a boundary layer on a plate in a wind tunnel) and the increase of dimension downstream is established experimentally.