1999
DOI: 10.1006/aphy.1998.5887
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A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities

Abstract: It is shown that tunnelling splittings in ergodic double wells and resonant widths in ergodic metastable wells can be approximated as easily-calculated matrix elements involving the wavefunction in the neighbourhood of a certain real orbit. This orbit is a continuation of the complex orbit which crosses the barrier with minimum imaginary action. The matrix element is computed by integrating across the orbit in a surface of section representation, and uses only the wavefunction in the allowed region and the sta… Show more

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Cited by 36 publications
(61 citation statements)
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“…which is a special case of a similar symmetry of F [15]. This symmetry is a reflection of the fact that the tunnelling orbit is periodic with an imaginary period and so complex conjugation is equivalent to timereversal.…”
Section: A the Tunnelling Operatormentioning
confidence: 91%
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“…which is a special case of a similar symmetry of F [15]. This symmetry is a reflection of the fact that the tunnelling orbit is periodic with an imaginary period and so complex conjugation is equivalent to timereversal.…”
Section: A the Tunnelling Operatormentioning
confidence: 91%
“…We first describe a tunnelling operator defined in [15] which relates tunnelling rates to the properties of wavefunctions in the allowed region. We then outline how this tunnelling operator is used to derive distributions for tunnelling rates in the absence of scarring.…”
Section: Tunnelling Statistics Without Scarringmentioning
confidence: 99%
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