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.     

Superballistic wavepacket spreading in double kicked rotors

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.     

Fractional variant Planck's over 2pi scaling for quantum kicked rotors without Cantori

Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length L) characterized by fractional variant Planck's over 2pi scaling; i.e., L approximately variant Planck's over 2pi;{2/3} in regimes and phase-space regions close to "golden-ratio" cantori. In contrast, in typical chaotic regimes, the scaling is integer, L approximately variant Planck's over 2pi;{-1}. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle, obtained by randomizing the phases every second kick; it has no Kol'mogorov-Arnol'd-Moser mixed-phase-space structures, such as golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but L approximately variant Planck's over 2pi;{-2/3}. A semiclassical analysis indicates that the variant Planck's over 2pi;{2/3} scaling here is of quantum origin and is not a signature of classical cantori.     

Recurrent versus diffusive dynamics for a kicked quantum system

We study the dynamics of a two-level quantum system subject to a time-dependent kicking perturbation modulated along the Thue-Morse sequence. For a nontrivial set of the parameters, the quantum autocorrelation function is explicitly calculated, and splits into a purely recurrent and a purely diffusive part. Furthermore, the diffusive part is directly related to the (singular continuous) correlation measure of the Thue-Morse sequence.     

Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.     

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.     

Localization-delocalization transition in chains with long-range correlated disorder

We investigated numerically localization properties of electron eigenstates in a chain with long-range correlated diagonal disorder. A tight-binding one-dimensional model with on-site energies exhibiting long-range correlated disorder (LCD) was used with various disorder strength W. LCD was defined so that it gave a power-law spectral density of the form S(k)αk^-p, where p determines the roughness of the potential landscape. Numerical results on the correlation length ξ of eigenstates shows the existence of the localization-delocalization transition at p=2. It is found that the critical values for disorder strength W_c and also the critical exponent ν for localization length change with the values of p.     

Leggett-Garg inequality with a kicked quantum pump

A kicked quantum nondemolition measurement is introduced, where a qubit is weakly measured by pumping current. Measurement statistics are derived for weak measurements combined with single-qubit unitary operations. These results are applied to violate a generalization of the Leggett-Garg inequality. The violation is related to the failure of the noninvasive detector assumption, and may be interpreted as either intrinsic detector backaction, or the qubit entangling the microscopic detector excitations. The results are discussed in terms of a quantum point contact kicked by a pulse generator, measuring a double quantum dot.     

Spectral properties of a periodically kicked quantum Hamiltonian

We study the spectral properties of the Floquet operator for the periodically kicked HamiltonianH(t) =H ₀+ ₊ ^– (t–nT),H ₀ being self-adjoint and pure point. We show that the Floquet operator is pure point for almost every , if is cyclic forH ₀ and has absolutely convergent expansion in the basis of eigenstates ofH ₀. When this last condition is not satisfied, the Floquet operator can have a continuous spectrum, as we show by an example.     

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.     

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.     

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.     

Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interaction that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.     

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.     

Classical and quantum dynamics of a kicked relativistic particle in a box

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.