A Bäcker et al 2002 Nonlinearity 15 1417 doi:10.1088/0951-7715/15/5/304
Orbit bifurcations and wavefunction autocorrelations
A Bäcker1, J P Keating2 and S D Prado3
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It was recently shown (Keating J P and Prado S D 2001 Proc. R. Soc. A 457 1855–72) that, in the semiclassical limit, the scarring of quantum eigenfunctions by classical periodic orbits in chaotic systems may be dramatically enhanced when the orbits in question undergo bifurcation. Specifically, a bifurcating orbit gives rise to a scar with an amplitude that scales as 
α and a width that scales as ω, where α and ω are bifurcation-dependent scar exponents whose values are typically smaller than those (α = ω = ½) associated with isolated and unstable periodic orbits. We here analyse the influence of bifurcations on the autocorrelation function of quantum eigenstates, averaged with respect to energy. It is shown that the length-scale of the correlations around a bifurcating orbit scales semiclassically as 1−α, where α is the corresponding scar amplitude exponent. This imprint of bifurcations on quantum autocorrelations is illustrated by numerical computations for a family of perturbed cat maps.
- PACS
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05.45.Mt Quantum chaos; semiclassical methods
- MSC
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81Q50 Quantum chaos (See also 37Dxx)
37M20 Computational methods for bifurcation problems
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 5 (September 2002)
Received 5 April 2002, in final form 18 June 2002
Published 15 July 2002
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Orbit bifurcations and wavefunction autocorrelations
A Bäcker et al 2002 Nonlinearity 15 1417
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