Abstract

AbstractIn this chapter, we report on a method to compute chaotic eigenfunctions in narrow energy windows using very efficient semiclassical basis sets. The basis elements are formed by scar functions, which are wave functions localized over unstable periodic orbits. The basis size is of the same order of the number of computed eigenfunctions and is given by the ratio between the Heisenberg and the Ehrenfest times. The accuracy of the developed method is assessed by calculating the eigenfunctions associated with the one-dimensional irreducible representations of a coupled two-dimensional quartic oscillator with a high degree of chaoticity.KeywordsChaotic eigenvectorEigenenergyScar functionTube functionSemiclassical approximationBohr–Sommerfeld quantizationGram–Schmidt selective methodBasis setQuartic potentialIrreducible representation

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.