Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1998-10-10
Nonlinearity 12, R1 (1999).
Nonlinear Sciences
Chaotic Dynamics
22 pages, 15 figures, invited review paper for Nonlinearity
Scientific paper
10.1088/0951-7715/12/2/009
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics framework leads to predictions about statistical long-time and stationary properties of quantum systems with chaotic classical analogues. Many long-time quantum properties can be quantitatively understood using only short-time classical dynamics information; these include wavefunction intensity distributions, intensity correlations in phase space and correlations between wavefunctions, and distributions of decay rates and conductance peaks in weakly open systems. Strong deviations from random matrix theory are predicted and observed in the presence of short unstable periodic orbits.
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