Ruelle resonances in kicked quantum spin chain

We study exponential decay of high temperature time correlation functions in a non-integrable quantum spin chain problem, namely Ising spin 1/2 chain kicked with tilted homogeneous magnetic field. For this purpose we define a master propagator over a suitable banach space of quantum observables (quantum many-body analogue of Perron–Frobenius operator) whose leading eigenvalue determines the asymptotic decay of correlations. This is demonstrated with explicit calculation for which a fast algorithm for the construction of the master propagator is developed.     

Classical and quantum localization and delocalization in the Fermi accelerator,kicked rotor and two-sided kicked rotor models

The phenomena of dynamical localization, both classical and quantum, are studied in the Fermi accelerator model. The model consists of two vertical oscillating walls and a ball bouncing between them. The classical localization boundary is calculated in the case of "sinusoidal velocity transfer" [A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, Berlin, 1983)] on the basis of the analysis of resonances. In the case of the "sawtooth" wall velocity we show that the quantum localization is determined by the analytical properties of the canonical transformations to the action and angle coordinates of the unperturbed Hamiltonian, while the existence of the classical localization is determined by the number of continuous derivatives of the distance between the walls with respect to time. (c) 1996 American Institute of Physics.     

Quantum resonances of the kicked rotor and the SU(q) group

The quantum kicked rotor map is embedded into a continuous unitary transformation generated by a time-independent quasi Hamiltonian. In some vicinity of a quantum resonance of order q, we relate the problem to the regular motion along a circle in a (q(2)-1) component inhomogeneous "magnetic" field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance.     

High-order quantum resonances observed in a periodically kicked Bose-Einstein condensate

We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.     

State reconstruction of the kicked rotor

We propose two experimentally feasible methods based on atom interferometry to measure the quantum state of the kicked rotor.     

Superballistic wavepacket spreading in double kicked rotor

We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.     

Theory of the Anderson transition in the quasiperiodic kicked rotor

We present the first microscopic theory of transport in quasiperiodically driven environments ("kicked rotors"), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of a dimensionless Planck constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we describe the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a "supermetal." We discuss the ensuing possibility of a metal-supermetal quantum phase transition.     

On kicked quantum systems

The time evolution of a multi-dimensional quantum system which is kicked at random or periodically with a potential is obtained. An interesting aspect of the evolution is that if the operator corresponding to the potential has invariant subspaces (this is characteristic of multi-dimensional problems), the system evolves in these invariant subspaces, i.e., each evolution in the subspaces is independent and there cannot be any mixing between the states of these subspaces.     

Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation.Recently,a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information.This paper studies the behaviours of quantum Fisher information in the quantum kicked top model,whose classical correspondence can be chaotic.It finds that,first,detected by quantum Fisher information,the quantum kicked top is entangled whether the system is in chaotic or in regular case.Secondly,the quantum Fisher information is larger in chaotic case than that in regular case,which means,the system is more sensitive in the chaotic case.     

Multi-dimensioned intertwined basin boundaries and the kicked double rotor

Using two examples, a four-dimensional kicked double rotor and a simple noninvertible one-dimensional map, we show that basin boundary dimensions can be different regions of phase space. For example, they can be fractal or not fractal depending on the region. In addition, we show that these regions of different dimension can be intertwined on arbitrarily fine scale. We conjecture, based on these examples, that a basin boundary typically can have at most a finite number of possible dimension values.     

On periodically kicked quantum systems

The time evolution of a multi-dimensional system which is kicked periodically with a potential is obtained. The most interesting aspects of the investigation are (i) if the operator corresponding to the potential has invariant subspaces (a characteristic property of multi-dimensional systems), the states belonging to these subspace in its evolution are confined to these invariant subspaces respectively and there cannot be any mixing of states between these subspaces. Further, (ii) it leads to the existence of quasi-stationary states (determined again by the potential) which evolves independent of other similar quasi-stationary states. The method followed in the paper is the direct integration of the Schrödinger equation and then to construct the wave function from the initial wave function.     

The periodically kicked quantum spin

It is shown that the same kind of deterministic chaos that occurs in classical systems can occur in certain quantum mechanical, many-body systems. The example of the physical realization of the periodically kicked quantum spin (PKQS) is considered in detail. The quantum mechanical equations of motion for this system can be converted into the three-dimensional PKQS map, which exhibits deterministic chaos and Arnold diffusion. Although the case of quantum spin s= 1/2 is assumed, it is shown that the same map results for s=1 (but not for s>/=3/2), and for a suitably chosen classical particle with orbital angular momentum. A simple generalization of the PKQS model gives rise to stochastic webs on the surface of the unit sphere very similar to the Zaslavsky stochastic webs in a plane.     

Localization and fluctuations in quantum kicked rotors

We address the issue of fluctuations, about an exponential line shape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter k and exhibit self-similarity for certain values of the quasienergy. For given k, the asymptotic localization length is a good characteristic of the localized line shapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances." These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.     

周期驱动的Harper模型的量子计算鲁棒性与量子混沌

以周期驱动的量子Harper(quantum kicked Harper, QKH)模型为例，研究复杂量子动力系统的量子计算在各种干扰下的稳定性.通过对Floquet算子本征态的统计遍历性及其Husimi函数的分析，比较随机噪声干扰和静态干扰对量子计算不同程度的影响.进一步的保真度摄动分析表明，在随机噪声干扰下保真度随系统演化呈指数衰减，而静态干扰下的保真度为高斯衰减，并通过数值计算得到了干扰下的可信计算时间尺度.与经典混沌仿真中误差使状态产生指数分离不同，量子计算对状态干扰的稳定性和仿真模型的动力学特性无关. 关键词： 量子Harper模型 量子计算 量子混沌 保真度     

量子Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法,研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明,一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比,在干扰强度小于某一阈值时,耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降;而在干扰强度大于该阈值时,静态干扰下的可信计算时间尺度下降更快. 关键词： 量子计算 量子Harper模型 主方程 量子Monte Carlo方法     

量子Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法，研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明，一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比，在干扰强度小于某一阈值时，耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降；而在干扰强度大于该阈值时，静态干扰下的可信计算时间尺度下降更快.     

A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model

In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that applies only in the neighborhoods of the lowest two quantum resonances, the proposed theory is applicable in the neighborhoods of all quantum resonances in principle by considering the quantum effect of the free rotation at a quantum resonance. In particular, i...