Orbit bifurcations and wavefunction autocorrelations

A Backer, JP Keating, SD Prado

Research output: Contribution to journalArticle (Academic Journal)

4 Citations (Scopus)

Abstract

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 h(alpha) and a width that scales as h(omega), where alpha and omega are bifurcation-dependent scar exponents whose values are typically smaller than those (alpha = omega = (1)/(2)) 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 h(1-alpha), where alpha 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.
Translated title of the contributionOrbit bifurcations and wavefunction autocorrelations
Original languageEnglish
Pages (from-to)1417 - 1433
JournalNonlinearity
Volume15 (5)
Publication statusPublished - Sep 2002

Bibliographical note

Publisher: IOC Publishing Ltd
Other identifier: IDS number 596XA

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    Backer, A., Keating, JP., & Prado, SD. (2002). Orbit bifurcations and wavefunction autocorrelations. Nonlinearity, 15 (5), 1417 - 1433.