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The quantum localization of chaotically diffusive classical motion is reviewed, using the kicked rotator as a simple but instructive example. The specific quantum steady state, which results from statistical relaxation in the discrete spectrum, is described in some detail. A new phenomenological...
Nonlinear wave phenomena are often characterized by the appearance of ‘‘solitary wave coherent structures’’ traveling at speeds determined by their amplitudes and morphologies. Assuming that time intervals exist in which these structures are essentially noninteracting, a method for...
The dynamical behavior of two coupled cells or reactors is described. The cells are coupled by diffusion, e.g., through a semipermeable membrane, and the chemical reactions and initial or feed concentrations of all species are the same in the two cells. Each cell has only a single stable steady...
The periodic forcing of nonlinear oscillations can often be cast as a problem involving self‐maps of the circle. Consideration of the effects of changes in the frequency and amplitude of the periodic forcing leads to a problem involving the bifurcations of circle maps in a two‐dimensional...
The field of quantum chaos has recently focused attention on the quantum description of chaotic scattering processes. The new physical intuition, analytical methods, and numerical tools developed in the study of the quantum behavior of classically chaotic bound systems, like quantum billiards or...
When a nonlinear crystal is placed within a multimode solid‐state laser cavity, deterministic fluctuations are induced in the output intensity. In this paper, the results of our studies of the intensity noise in a diode pumped, intracavity frequency doubled Nd:YAG (neodymium doped yttrium...
The relation between the spectrum of a generalized quasienergy operator and the stability of quantum systems driven by quasiperiodic time‐dependent forces is discussed.
The description of the Gelfand–Tsetlin model is presented as excerpts from the author’s diploma dissertation on the mappings of a circle to itself.
The ionization of the highly excited hydrogen atom in a strong external microwave field is a classically chaotic, near‐classical quantum system for microwave frequencies somewhat below the initial Kepler electron orbit frequency. The addition of microwave noise is found to reduce the sinewave...
In this paper a review is given of experimental techniques in chaotic dynamics of solid mechanical systems based on modern ideas of nonlinear dynamics. These methods include Poincaré maps, double Poincaré sections, symbol dynamics, and fractal dimension. The physical problems discussed include...
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