Spectra of regular quantum graphs

We consider a class of simple quasi-one-dimensional classically nonintegrable systems that capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is sufficiently simple to allow a detailed investigation of both classical and quantum regimes. Despite their classical chaoticity, these systems exhibit a “nonintegrable analogue” of the Einstein-Brillouin-Keller quantization formula that provides their spectra explicitly, state by state, by means of convergent periodic orbit expansions.     

Spectroscopy of collective excitations in interacting low-dimensional many-body systems using quench dynamics

We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.     

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.     

Quantum effects of periodic orbits for the kicked top

We analyze traces of powers of the time evolution operator of a periodically kicked top. Semiclassically, such traces are related to periodic orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovered via a Fourier transform. A breakdown of the stationary phase approximation is detected. The quasi energy spectrum remains elusive due to lack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coefficients of the characteristic polynominal of the Floquet operator. Statistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.     

Hierarchical structures in the phase space and fractional kinetics: II. Immense delocalization in quantized systems

Anomalous transport due to Levy-type flights in quantum kicked systems is studied. These systems are kicked rotor and kicked Harper model. It is confirmed for a kicked rotor that there exist special "magic" values of a control parameter of chaos K=K(*)=6.908 745 em leader for which an essential increasing of a localization length is obtained. Functional dependence of the localization length on both parameter of chaos and quasiclassical parameter h is studied. We also observe immense delocalization of the order of 10(9) for a kicked Harper model when a control parameter K is taken to be K(*)=6.349 972. This "magic" value corresponds to special phase space topology in the classical limit, when a hierarchical self-similar set of sticky islands emerges. The origin of the effect is of the general nature and similar immense delocalization as well as increasing of localization length can be found in other systems. (c) 2000 American Institute of Physics.     

Integrability of the Rabi model

The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries; the generalized Rabi model is the first example of a nonintegrable but exactly solvable system.     

Experimental demonstration of localization in the frequency domain of mode-locked lasers with dispersion

Mode-locked lasers with intracavity dispersion are experimentally shown to exhibit localization behavior in their frequency domain. The localization, with its typical exponential spectrum structure, is analogous to that which occurs for the quantum kicked rotor. The experimental demonstration of our optical kicked rotor is done with a long mode-locked dispersive fiber laser. The localization effect sets a basic limit on the spectrum bandwidth and the minimum pulse width in such lasers. It also provides a special experimental test bed for the study of optical kicked rotors and localization effects.     

Symmetry versus degree of level repulsion for kicked quantum systems

Quantum systems capable of chaotic motion in the classical limit can display linear, quadratic, or quartic level repulsion. For a given (time independent or time dependent) Hamiltonian the degree of level repulsion is determined by the full group of its unitary and antiunitary symmetries. We establish this connection for kicked systems, using Wigner's theory of corepresentations, and the appropriate generalization of Pechukas' phase space flow. We illustrate the theory in terms of two systems of kicked spins both of which are time reversal invariant, one showing linear and the other quadratic level repulsion.     

Exact Solutions of the Coupled KdV system via a Formally Variable Separation Approach

Most of the nonlinear physics systems are essentially nonintegrable.There in no very doog analytical approach to solve nonintegrable system.The variable separation approach is a powerful method in linear physics.In this letter,the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation.The method is valid not only for integrable models but also for nonintegrable models.Taking a nonintegrable coupled KdV equation system as a simple example,abundant solitary wave solutions and conoid wave solutions are revealed.     

Effect of temporal disorder on wave packet dynamics in one-dimensional kicked lattices

Inspired by the recent experimental progress in noisy kicked rotor systems,we investigate the effect of temporal disorder or quasi-periodicity in one-dimensional kicked lattices with pulsed on-site potential.We found that,unlike the spatial disorder or quasi-periodicity which usually leads to localization,the effect of the temporal one is more complex and depends on the spatial configuration.If the kicked on-site potential is periodic in real space,then the wave packet will stay diffusive in the presence of temporal disorder or quasi-periodicity.On the other hand,if the kicked on-site potential is spatially quasi-periodic,then the temporal disorder or quasi-periodicity may lead to a shift of the transition point of the dynamical localization and destroy the dynamical localization in a certain parameter range.The results we obtained can be readily tested by experiments and may help us better understand the dynamical localization.     

Transport in quasi one-dimensional spin-1/2 systems

We present numerical results for the spin and thermal conductivity of one-dimensional (1D) quantum spin systems. We contrast the properties of integrable models such as the spin-1/2 XXZ chain against nonintegrable ones such as frustrated and dimerized chains. The thermal conductivity of the XXZ chain is ballistic at finite temperatures, while in the nonintegrable models, this quantity is argued to vanish. For the case of frustrated and dimerized chains, we discuss the frequency dependence of the transport coefficients. Finally, we give an overview over related theoretical work on intrinsic and extrinsic scattering mechanisms of quasi-1D spin systems.     

The periodically kicked rotator: Recurrence and/or energy growth

We explore the properties of the quantum kicked rotator, its classical equivalent being the standard map. Its behavior, as found by computer studies, depends very much on the strength of the external forcing. At low strength it is seemingly recurrent in the sense of Hogg and Huberman. However, its energy increases with time at large forcings. For quantum systems, a unitary map defines the evolution over one period of time. The spectrum of this map in an infinite space does not seem to change continuously when one approaches the ratio of the frequencies of the external and of the unperturbed system by rational approximations of the golden mean.     

Supersolitons: solitonic excitations in atomic soliton chains

We show that, by tuning interactions in nonintegrable vector nonlinear Schr?dinger equations modeling Bose-Einstein condensates and other relevant physical systems, it is possible to achieve a regime of elastic particlelike collisions between solitons. This would allow one to construct a Newton's cradle with solitons and supersolitons: localized collective excitations in solitary-wave chains.     

Dynamic Behavior and Quasi—energy Spectrum of Multiband Superlattice Bloch Electrons in Quantum Kicked Potential

In this paper,we study the dynamic behavior and quasi-energy spectrum of multiband superlattics Bloch electrons in quantum kicked potential.We show analytically and numerically the avoided crossing and band suppression about the quasi-energy spectrum.The dynamic nonlocalization,and the electron oscillation behavior between two bands.     

Coherent structures and entropy in constrained, modulationally unstable, nonintegrable systems

Many studies have shown that nonintegrable systems with modulational instabilities constrained by more than one conservation law exhibit universal long time behavior involving large coherent structures in a sea of small fluctuations. We show how this behavior can be explained in detail by simple thermodynamic arguments.     

Kink-antikink collisions in the φ⁶ model

We study kink-antikink collisions in the one-dimensional nonintegrable scalar φ? model. Although the single-kink solutions for this model do not possess an internal vibrational mode, our simulations reveal a resonant scattering structure, thereby providing a counterexample to the standard belief that the existence of such a mode is a necessary condition for multibounce resonances in general kink-antikink collisions. We investigate the two-bounce windows in detail, and present evidence that this structure is caused by the existence of bound states in the spectrum of small oscillations about a combined kink-antikink configuration.     

Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems. In a similar way as for near-integrable tunneling, such resonances induce couplings between regular states within the islands and states that are supported by the chaotic sea. On the basis of this mechanism, we derive a semiclassical expression for the average tunneling rate, which yields good agreement in comparison with the exact quantum tunneling rates calculated for the kicked rotor and the kicked Harper.     

A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

We study the localized coherent structures ofa generally nonintegrable (2 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.     

On solitary-wave interaction

We study analytically the interaction of the solitary waves of the regularized long-wave equation proposed by Peregrine and Benjamin et al. It is shown in the long-wave limit that the solitary waves interact inelastically, and that a new solitary wave as well as a radiation tail are generated as a result of the interaction. The result agrees with the numerical observation made by Bona et al. The analysis presented here can also be applied to the general weakly dispersive nonlinear wave systems, and it shows that the interaction property holds commonly for the nonintegrable systems.     

A super-Ohmic energy absorption in driven quantum chaotic systems

We consider energy absorption by driven chaotic systems of the symplectic symmetry class. According to our analytical perturbative calculation, at the initial stage of evolution the energy growth with time can be faster than linear. This appears to be an analog of weak anti-localization in disordered systems with spin-orbit interaction. Our analytical result is also confirmed by numerical calculations for the symplectic quantum kicked rotor.