RT Journal Article
SR Electronic
T1 Fringes decorating anticaustics in ergodic wavefunctions
JF Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO Proc R Soc Lond A Math Phys Sci
FD The Royal Society
SP 279
OP 288
DO 10.1098/rspa.1989.0082
VO 424
IS 1867
A1
YR 1989
UL http://rspa.royalsocietypublishing.org/content/424/1867/279.abstract
AB The probability density Π is calculated for quantum eigenstates near spatial boundaries of classically chaotic regions. By contrast with integrable systems, for which the classical Π diverges on classical boundaries, which are caustics, in chaotic systems the classical Π does not diverge but vanishes abruptly in a way that depends on the number of freedoms N; the boundaries are anticaustics. Quantum mechanics softens anticaustics, to give Π in terms of a set of canonical diffraction patterns, one for each N; these are studied in detail. The appropriate definition of Π involves averaging over eigenstates in an energy range larger than O(h) but smaller than O(h⅔) (where h is Planck’s constant), that is over a range of ∆N states near the Nth, where N1-1/N ≪ ∆N ≪ N1-⅔N.