Abstract
The way in which quantum eigenstates are influenced by the closed orbits of a chaotic classical system is analysed in phase space
x
═ (
q, p
) through the spectral Wigner function
W
(
x
;
E, ∊
). This is a sum over Wigner functions of eigenstates within a range
∊
of energy
E
. In the classical limit,
W
is concentrated on the energy surface and smoothly distributed over it. Closed orbits provide oscillatory corrections (scars) for which explicit semiclassical formulae are calculated. Each scar is a fringe pattern decorating the orbit. As
x
moves off the energy surface the fringes form an Airy pattern with spacing of order
h
⅔
. As
x
moves off the closed orbit the fringes form a complex gaussian with spacing
h
½
.
Cited by
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