Signatures of chaos in the modulus and phase of time-dependent wave functions

Boon Leong Lan, David M. Wardlaw

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


For a classically chaotic two-dimensional bound system, based on the assumption that an initially-well-localized, semiclassical wave packet can be represented by a superposition of a large number of random plane waves at fixed times, we show that the modulus and phase of the wave function are independent random functions having a Rayleigh and a uniform one-point spatial distribution function, respectively. These predictions are confirmed through our numerical wave-packet study for one-quarter of the Sinai billiard. Streamline vortices can form around wave-function nodes, a fact first discovered by Dirac in 1931. For a classically chaotic billiard, the random plane-wave superposition approximation predicts that both the number of nodal points and the maximum number of vortices in a wave packet with initial wave number k is N, where N refers to the Nth eigenstate with wave number kN which is closest to k.

Original languageEnglish
Pages (from-to)2176-2179
Number of pages4
JournalPhysical Review E
Issue number3
Publication statusPublished - 1993
Externally publishedYes

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