CHAOS: |
The dynamics of systems that are described by simple models
exhibiting motion that is complicated. The complexity results of exponential separation (in time) of neighboring trajectories. Since Chaos is defined in terms of trajectories, it is a classical concept. In particular the decay of correlations was studied for systems where the entire phase space, or part of it, is chaotic. |
QUANTUM CHAOS: |
The exploration of the quantum dynamics of systems that are chaotic in
the classical limit. In this field the fingerprints of Chaos (that is a classical term) in the quantum dynamics are studied. Some classical chaotic systems exhibit diffusion in phase space. For the corresponding quantum systems this diffusion is suppressed by a mechanism that is similar to Anderson localization in disordered solids. The pseudo-randomness of chaotic systems plays the role of true randomness in the disordered solids. Therefore Anderson localization is a fingerprint of classical chaos. The quantal suppression of chaos was observed in experiments in Atom Optics as well as in Classical Wave Optics. The standard fingerprints of chaos are found in the energy level statistics. The studies of these were extended to wave functions, Wigner functions and matrix elements. The spectral statistics of systems that are intermediate between regular and chaotic ones were studied in detail. |
ATOM OPTICS: |
The exploration of the dynamics of atoms that are sufficiently cold,
so that their wave properties dominate their center of mass dynamics. Anderson localization, that was predicted for chaotic systems, was observed experimentally for cold sodium and cesium atoms. At a later stage coherent acceleration of such atoms was observed. It was explained in the framework of a pseudo-classical (chaotic) theory, where the separation of the driving frequency from resonance plays the role of Planck's constant. The dynamics were found to be determined by the number theoretical properties of the gravitational constant (in appropriate dimensionless units). A theory for the modes of ionic crystals was developed. Oscillating potentials, like the one of the Kapitza pendulum, that are rapidly oscillating, relevant for Atom Optics, were studied classically and the studies were extended to Quantum Mechanics. |
PSEUDO-RANDOMNESS: |
The exploration of the question when deterministic sequences look like
random ones. |
QUANTUM DISSIPATION: |
Description of dissipation in a regime where the quantum mechanical properties
of the system are important. |
APPLICATION of the THEORY of DYNAMICAL SYSTEMS to problems in Computer Science and Medicine. |
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