By Chris Engelbrecht Summer School on Theoretical Physics 1992 blydepoor, W. D. Heiss, W. D. Heiss
In the past the real thought of quantum chaos has remained slightly ailing outlined. This quantity tackles the ever-present borderline among classical and quantum mechanics, learning particularly the semiclassical restrict of chaotic structures. the results of affliction from dynamics and their relation to stochastic structures, quantum coherence results in mesoscopic platforms, and the correct theoretical methods are fruitfully mixed during this quantity. the most important paradigms of what's referred to as quantum chaos, random matrix conception and purposes to condensed subject and nuclear physics are provided. unique discussions of experimental paintings with specific emphasis on atomic physics are integrated. The publication is very urged for graduate-student seminars. - this article refers to an out of print or unavailable version of this name.
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52; E = < n 2 > / 2 is the energy. Solid line - a single run; dashed and dotted lines - different averages over 104 runs; straight line - classical diffusion (after rtef. ). principle. ) as well as analitically . 56. 4, is in a good agreement with the classical dependence even for those K values where a simple theory fails. We call tn the diffusion or (statistical) relaxation time scale. This similarity to the classical chaos is, however, only partial. Unlike the classical one the quantum diffusion was found to be perfectly stable dynamically.
In the opposite limiting case A >> I ( D >> C) the relaxation time scale, being finite, is nevertheless long enough for the relaxation to the ergodic steady state to be accomplished. In this case the final steady state is close to that in classical mechanics. The same is true for conservative systems of two freedoms like billiards or cavities. 11)). 5. F i n i t e - t i m e in discrete statistical spectrum. relaxation We turn now to a more accurate description of the quantum relaxation in 27 the standard map.
Both effects Seem to cancel, and the integral repulsion vanishes. 22). However, this conclusion is very sensitive to the exact relaxation law. . To conclude, this question certainly requires further studies. [60,85,86]. 18) with the entropy averaged over all eigenstates. The dependence can be approximately described by two expressions /~/]. 21) has been identified. 1) for localized eigenstates. On a torus it becomes ~mCn) ~ 1+ Ssinh(1/$) ) cosh Jm ? ! 21). 1). 21) has the nature of a scaling in the sense that fin and fl ~ fin depend on the ratio ~ = I / C = D / 2 C only, whatever the underlying mechanism could be.