Fluctuations and decoherence in chaos-assisted tunneling

We study quantum dynamical tunneling between two symmetry-related islands of stability in the phase space of a classically chaotic system. The setting for these experiments is the motion of carefully prepared samples of cesium atoms in an amplitude-modulated standing wave of light. We examine the dependence of the tunneling dynamics on the system parameters and indicate how the observed features provide evidence for chaos-assisted (three-state) tunneling. We also observe the influence of a noisy perturbation of the standing-wave intensity, which destroys the tunneling oscillations, and we show that the tunneling is more sensitive to the noise for a smaller value of the effective Planck constant.     

二维形变谐振子系统中的量子经典对应

通过引入等效普朗克常数,将量子系统中基本动力学变量的期望值和经典系统中基本动力学变量的精确值的时间演化行为相比较,分析了两者产生差异的因素,规则运动主要是和量子效应有关,而混沌运动则是和动力学效应有关,即与系统的动力学对称性破坏相联系.在此基础上,比较了量子相空间测不准度和李雅谱诺夫指数,给出了令人满意的说明.     

Crossover from diffusive to ballistic transport in periodic quantum maps

We derive an expression for the mean square displacement (MSD) of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, t, and Planck’s constant, h, and allows a study of both the long time, t→∞, and semi-classical, h→0, limits taken in either order. We evaluate the expression using random matrix theory as well as numerically, and observe good agreement between both sets of results. The long time limit shows that particle transport is generically ballistic for any fixed value of Planck’s constant. However, for fixed times, the semi-classical limit leads to diffusion. The mean square displacement for non-zero Planck’s constant, and finite time, exhibits a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck’s constant. We argue that these results are generic for a large class of 1D quantum random walks, similar to the quantum multi-baker, and that a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Some connections between our work and the other literature on quantum random walks are discussed. These walks are of some interest in the theory of quantum computation.     

Structure of Regions of Regular Motion in the Phase Space of Channeled Electrons

The motion of electrons in the axial channeling mode in the [100] direction of a Si crystal can be regular and chaotic (depending on the initial conditions). The contribution of regions of regular and chaotic dynamics to the quasiclassical density of energy levels of the transverse motion of electrons is found in this paper. The obtained values are used as parameters of the Berry—Robnik distribution describing the level spacing statistics in the case of the coexistence of regions of regular and chaotic motion.     

量子无规运动与核耗散

从动力学对称性观点出发考察了量子规则运动与无规运动 .用能级动力学研究了从量子规则运动向量子无规运动的过渡 ,给出了导致能级混沌的条件 ,揭示了造成能级混沌的机制 .用混沌态矢的特征解释了原子核的各态历经集体态的衰变特性 .研究了重离子碰撞中核耗散与动力学对称性破坏之间的关系. Quantum regular and irregular motions are investigated from the viewpoint of dynamical symmetry. The transition from quantum regular motion to chaotic motion is studied by level dynamics and computer experiments. The conditions for onset of quantum chaos are presented.The mechanism for causing chaotic level spectrum is unveiled. The decay behavior of the nuclear ergodic collective states is explained in terms of the peculiar property of chaotic states. The connection between nuclear...     

Motion of vortices outside a cylinder

The problem of motion of the vortices around an oscillating cylinder in the presence of a uniform flow is considered. The Hamiltonian for vortex motion for the case with no uniform flow and stationary cylinder is constructed, reduced, and constant Hamiltonian (energy) curves are plotted when the system is shown to be integrable according to Liouville. By adding uniform flow to the system and by allowing the cylinder to vibrate, we model the natural vibration of the cylinder in the flow field, which has applications in ocean engineering involving tethers or pipelines in a flow field. We conclude that in the chaotic case forces on the cylinder may be considerably larger than those on the integrable case depending on the initial positions of vortices and that complex phenomena such as chaotic capture and escape occur when the initial positions lie in a certain region.     

Classical spin dynamics of anisotropic Heisenberg dimmers

In the present work we study the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of an external magnetic field using the Landau-Lifshitz equation. The interaction between particles is through the exchange energy. We study both conservative and dissipative cases. In the first one, we characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and bifurcation diagrams. In particular, we explore the dependence of the largest Lyapunov exponent respect to the magnitude of applied magnetic field and exchange constant. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated topology of intricately intermingled chaotic and regular regions. In the dissipative case, we calculate the final saturation states as a function of the magnitude of the applied magnetic field, exchange constant as well as the anisotropy constants.     

Terahertz radiation from carbon nanorings in external collinear constant and varying electric fields

We consider the response of a quasi-one-dimensional ballistic carbon ring to the field of an electromagnetic wave propagating along the normal to the ring plane in the presence of a constant electric field collinear to the field of the wave. The dipole moment and the radiation intensity of the ring are calculated for the ballistic motion of a conduction electron. The possibility of implementation of regular periodic and chaotic regimes of ring emission under the action of external fields is demonstrated. The radiation spectrum of the ring is analyzed, and the dependence of the scattering cross section for an electromagnetic wave incident on the ring on its frequency and amplitude is calculated.     

SU(2)对称破缺下的氰化氘分子的混沌运动

用SU(2 )陪集表象来表示氰化氘分子 (DCN)两个耦合的伸缩振动模式 ,在混沌运动研究中 ,这是一个最简单的SU (2 )对称被破坏的模型。研究表明 ,当振动能量小于 1 2 5 0 2cm- 1 时 ,体系呈现规则运动 ;能量处于 1 2 5 0 2cm- 1 和 1 82 4 6cm- 1 之间 ,规则和混沌运动并存 ;能量高于 1 82 4 6cm- 1 时 ,体系呈现完全的混沌运动。同时 ,在庞加莱截面上观察到了周期 3轨道 ,由Sarkovskii定理 ,这意味着混沌的出现。另外还表明 ,D -C伸缩键的量子数激发决定体系的混沌运动     

Chaotic evolution of the coupled scalar fields system during inflation

In this paper we consider two coupled scalar fields during the inflation as a dynamical system. With the Poincaré section method, we investigate the evolution of the coupled scalar fields system. We find that the evolution of the system changes from a regular motion into a chaotic motion when the energy density and the coupling constant of the system increase.     

Dynamical entanglement as a signature of chaos in the semiclassical limit

The relationship between classically chaotic dynamics and the entanglement properties of the corresponding quantum system is examined in the semiclassical limit. Numerical results are computed for a modified kicked top, keeping the classical dynamics constant while investigating the entanglement for several versions of the corresponding quantum system characterized by a different value of the effective Planck constant ℏ _eff. Our findings indicate that as ℏ _eff → 0, the apparent signatures of classical chaos in the entanglement properties, such as characteristic oscillations in the time-dependence of the linear entropy, can also be obtained in the regular regime. These results suggest that entanglement is not a universal marker of chaotic dynamics of the corresponding classical system.     

Chaotic Motion of the cc System and a New Mechanism of J/Ø Suppression

Based on random matrix theory and reduced BS equation, it is found that the regular motion of cc system can be expected at a small value of color screening mass but the chaotic motion at a large one. It is shown that the level mixing due to color screening serves as a new mechanism resulting in J/Ø suppression. Moreover, this kind of suppression can occur before the color screening mass reaches its critical value for J/Ø dissociation. In addition, it is. implied that a strong J/Ø suppression is possible in the absence of dissociation of J/Ø.     

Classical study of the rovibrational dynamics of a polar diatomic molecule in static electric fields

We study the classical dynamics of a polar diatomic molecule in the presence of a strong static homogeneous electric field. Our full rovibrational investigation includes the interaction with the field due to the permanent electric dipole moment and the polarizability of the molecule. Using the LiCs molecule as a prototype, we explore the stability of the equilibrium points and their bifurcations as the field strength is increased. The phase space structure and its dependence on the energy and field strength are analyzed in detail. We demonstrate that depending on the field strength and on the energy, the phase space is characterized either by regular features or by small stochastic layers of chaotic motion.     

Nonlinear coherent dynamics of an atom in an optical lattice

We consider a simple model of the lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. The internal dynamics of the atom is governed by the laser field, which is treated as classical with a large number of photons. The center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degrees of freedom. The resulting Hamilton-Schrö dinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion, and the total atomic energy and the Bloch vector length are conserved during the interaction. In our previous papers, the motion of the atom has been shown to be regular or chaotic (in the sense of exponential sensitivity to small variations of the initial conditions and/or the system’s control parameters) depending on the values of the control parameters, atom-field detuning, and recoil frequency. At the exact atom-field resonance, the exact solutions for both the external and internal atomic degrees of freedom can be derived. The center-of-mass motion does not depend in this case on the internal variables, whereas the Rabi oscillations of the atomic inversion is a frequency-modulated signal with the frequency defined by the atomic position in the optical lattice. We study analytically the correlations between the Rabi oscillations and the center-of-mass motion in two limiting cases of a regular motion out of the resonance: (1) far-detuned atoms and (2) rapidly moving atoms. This paper is concentrated on chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that an atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential, or fly ballistically with weak chaotic oscillations of its momentum, or wander in the optical lattice, changing the direction of motion in a chaotic way. In the regime of chaotic wandering, the atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion-Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincaré mappings are constructed using the translational invariance of the standing laser wave. We find common features with typical nonhyperbolic Hamiltonian systems-chains of resonant islands of different sizes imbedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of the atomic trajectories sticking to boundaries of regular islands, which should have a great influence on atomic transport in optical lattices, is found and demonstrated numerically.     

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.     

Chaotic Motion of a Nucleon in Heavy Nuclei with Necked-in Shape

In the framework of two-center shell model the nearest neighboring level spacing distribution and spectral rigidity of the nucleon in heavy nuclei are calculated when the shape parameters are changed systematically. Two regions of shape parameter in which the chaotic motion of the nucleon occurs are found. It is shown that the chaotic motion appears not only in the heavy nuclei with oblate shapes but also in prolate ones with a considerable neck, which is quite different from the conclusions of Ref. [2]. Bohigas Giannoni Schmit conjecture is corroborated once again by the good quantum-classical correspondence of nucleonic regular (chaotic) motion. In addition, the present work suggests that nuclear dissipation is shape-dependent,strong dissipation is expected for medium or larger separations, and provides nuclear dissipation with a dynamical understanding.     

Quantum ratchets in dissipative chaotic systems

Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.     

variant Planck's over 2pi expansion for the periodic orbit quantization of chaotic systems

We report the results of a periodic orbit quantization of classically chaotic billiards beyond Gutzwiller approximation in terms of asymptotic series in powers of the Planck constant (or in powers of the inverse of the wave number kappa in billiards). We derive explicit formulas for the kappa(-1) approximation of our semiclassical expansion. We illustrate our theory with the classically chaotic scattering of a wave on three disks. The accuracy on the real parts of the scattering resonances is improved by one order of magnitude.     

Dissipative quantum chaos: transition from wave packet collapse to explosion

Using the quantum trajectories approach, we study the quantum dynamics of a dissipative chaotic system described by the Zaslavsky map. For strong dissipation the quantum wave function in the phase space collapses onto a compact packet which follows classical chaotic dynamics and whose area is proportional to the Planck constant. At weak dissipation the exponential instability of quantum dynamics on the Ehrenfest time scale dominates and leads to wave packet explosion. The transition from collapse to explosion takes place when the dissipation time scale exceeds the Ehrenfest time. For integrable nonlinear dynamics the explosion practically disappears leaving place to collapse.