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# Quantum Chaos in Extended Systems: Spreading Wave Packets and Avoided Band Crossings

12/1999;
Source: CiteSeer

ABSTRACT Introduction When studying the implications of a classical non-integrable limit on the spectral properties of a quantum system, one usually restricts attention to the case of a pure-point (or `discrete') spectrum [1, 2]. In this case, non-integrability of the classical limit leads to avoided crossings of energy levels when changing an external parameter. This is related to the fact that the distribution of energy levels of such a system generically has the properties predicted by Random Matrix Theory [2]. In general, however, the spectrum of a quantum system need not have a pure-point component only: e.g., periodic systems generically have an absolutely continuous (`band') spectrum and quasiperiodic systems often show all possible spectral types, including notably singular continuous components - often in form of a fractal spectrum. In the general case, if the classical limit is nonintegrable, in analogy to avoided level crossings in pure point spectra mentioned above, the cha

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