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Simulating quantum mechanical systems is known to be a difficult computational problem. In particular, for many-body quantum systems the size of the Hilbert space grows exponentially with the number of particles. On the other hand, the growth in memory requirement is only polynomial on a quantum computer, which is itself a many-body quantum system. Therefore, a quantum computer operating with only a few tens of qubits would outperform a classical computer. Moreover, quantum computers with only about ten qubits could efficiently simulate complex single-particle quantum dynamical systems.

We study the dynamics of a quantum particle in a triangular potential well under a monochromatic driving. We provide a purely quantal theory that accounts for the transition from localization to delocalization, without making reference to the chaotic transition occurring in the classical limit.

We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion by relating the degree of reversibility to the rate at which a quantum state acquires a more and more complicated structure during its time evolution. This complexity can be characterized by the number M(t) of harmonics of the (initially isotropic, i.e. M(0) = 0) Wigner function, which are generated by the time t. We show that, in contrast to the classical exponential increase, this number can grow after the Ehrenfest time tE not faster than linearly. It follows that if the motion is reversed at some arbitrary moment T immediately after applying an instant perturbation with intensity described by the parameter ξ, then there exists a critical perturbation strength, ξc ≈ √ 2/M(T ), below which the initial state is well recovered, whereas reversibility disappears when ξ & ξc(T ). In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model.

The localization phenomenon plays an essential role in the excitation of hydrogen atoms in microwave fields. The similarity of this phenomenon to Anderson localization, which has been established and discussed in previous papers, is here demonstrated in a transparent way by reducing the quantum dynamics to a one-dimensional pseudo-Anderson model. The effect of slight changes in the driving frequency on the ionization probability is numerically investigated on the quantum Kepler map; huge fluctuations are found, which persist down to a very fine frequency scale and have a qualitatively random nature. It is argued that such fluctuations are a counterpart of the mesoscopic fluctuations of solid-state physics, and that similar fluctuations should be expected any time, when some classical chaotic diffusive process is quantum-mechanically suppressed by dynamical localization.

A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well defined classical analog which can be easily obtained from the classical equations of motion. Therefore, the occupation numbers for single-particle states can be represented as a convolution of the classical SE with the quantum occupation number operator for non-interacting particles. The latter takes into account the wavefunctions symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers $n_s$ can be numerically found for a very large number of interacting particles. Using the model of interacting spins we demonstrate that this approach gives a correct description of $n_s$ even in a deep quantum region with few single-particle orbitals., 4 pages, 2 figures

We study the dynamics of a quantum rotator kicked according to the almost-periodic Fibonacci sequence. A special numerical technique allows us to carry on this investigation for as many as $10^{12}$ kicks. It is shown that above a critical kick strength the excitation of the system is well described by regular diffusion, while below this border it becomes anomalous, and sub-diffusive. A law for the dependence of the exponent of anomalous sub-diffusion on the system parameters is established numerically. The analogy between these results and quantum diffusion in models of quasi-crystal and in the kicked Harper system is discussed., 7 pages, 4 figures, submitted to Phys. Rev. E

Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit.

The basic principles of the laser are common knowledge by this time [1]. Furthermore, the laser has raised to a paradigm for synergetics [2],which provides the fertile framework for a unitary description of collective phenomena occurring in so many branches of science. Really,all concepts of synergetics apply to a deep understanding of the process of self-organization occurring in the dynamics of the atoms near the threshold for laser emission. Actually,by increasing the pump of the lasing atoms,they evolve from a regime of spontaneous emission,in which each atom radiates independently and the emitted radiation is incoherent,to a cooperative regime of stimulated emission,in which the radiation is coherent. This 2nd-order-like phase transition from noncooperative to cooperative behaviour occurs at a critical value of the pump parameter which plays the role of a control parameter for the system.

A simple numerical reversibility test which proves useful in exposing the chaotic nature of classical dynamical systems is applied to the quantum model of a hydrogen atom in a microwave field. The remarkable result is that, in spite of some apparent chaotic features, the quantum motion proves to be perfectly stable in contrast to the high instability of the classical chaotic motion.

In this paper we study the coherent interaction among a system of N electrons and two fields of the same frequency, namely a radiation field copropagating with the particles and a classical pump field which is counterpropagating.

Fidelity is a convenient tool to study the sensitivity of quantum motion under Hamiltonian perturbations. In this paper we first show that classical chaos can produce the dephasing necessary to suppress quantum interference, even in the absence of any environment. To this end we consider the fidelity of mixed states, which takes into account interference amplitudes, and directly relate its decay to the decay of an appropriate classical correlation function, which is totally unrelated to quantum phases. We then discuss the dephasing in a two-qubit system, induced by the coupling to a single -particle, deterministic chaotic environment. The latter is shown to behave as a pure dephasing many-body object which induces decoherence in the system; memory effects are also taken into account.