Scarring and the statistics of tunnelling

Details Scarring and the statistics of tunnelling Scarring and the statistics of tunnelling

2001-07-03

arxiv.org/abs/nlin/0107006v1

Ann. Phys. (N.Y.), vol.295, pp194-215 (2002).

Nonlinear Sciences

Chaotic Dynamics

20 pages, 4 figures, submitted to Ann. Phys

Scientific paper

10.1006/aphy.2001.6202

We show that the statistics of tunnelling can be dramatically affected by scarring and derive distributions quantifying this effect. Strong deviations from the prediction of random matrix theory can be explained quantitatively by modifying the Gaussian distribution which describes wavefunction statistics. The modified distribution depends on classical parameters which are determined completely by linearised dynamics around a periodic orbit. This distribution generalises the scarring theory of Kaplan [Phys. Rev. Lett. {\bf 80}, 2582 (1998)] to describe the statistics of the components of the wavefunction in a complete basis, rather than overlaps with single Gaussian wavepackets. In particular it is shown that correlations in the components of the wavefunction are present, which can strongly influence tunnelling-rate statistics. The resulting distribution for tunnelling rates is tested successfully on a two-dimensional double-well potential.

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