Classical-quantum correspondence for chaotic motion

Journal Article · Sat May 01 04:00:00 EDT 1993 · Bulletin of the American Physical Society

OSTI ID:281463

Heller, E J

We examine semiclassical propagation of nonstationary states. The fundamental object is the 1928 time dependent Van Vleck semiclassical Green`s function, as modified by Gutzwiller in 1967. This direct approach to semiclassical quantum mechanics has received very little attention over the years. The problems of evaluating the Green`s function (finding all trajectories which go from x{prime} to x in time t, for every x, x{prime}, and t sounds foreboding) and the development of caustics at an alarming rate in chaotic systems, may have suppressed its use. We have developed several strategies for evaluating it efficiently, including for chaotic dynamics. We found it can be used to accurately propagate smooth wave functions in spite of the caustics. The smooth wave function has the effect of strongly damping the caustics and leaving an accurate propagated state. Moreover many of the contributions to the semiclassical amplitude are legal, and allow a much longer time scale for breakdown of the semiclassical propagation than had previously been thought. This has allowed us to extract accurate spectra and eigenstates for chaotic dynamics in the stadium billiard and to calculate a complete molecular electronic absorption spectrum for two nonlinearly interacting vibrational modes, including line intensities and positions, using only classical trajectory input.

• OSTI ID: 281463
• Report Number(s): CONF-9305421--
• Journal Information: Bulletin of the American Physical Society, Journal Name: Bulletin of the American Physical Society Journal Issue: 3 Vol. 38; ISSN BAPSA6; ISSN 0003-0503
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLASSICAL MECHANICS
EXCITED STATES
GREEN FUNCTION
MOLECULES
QUANTUM MECHANICS
RANDOMNESS
VIBRATIONAL STATES
WAVE FUNCTIONS