Scar and antiscar quantum effects in open chaotic systems

We predict and numerically observe strong periodic orbit effects in the pro perties of weakly open quantum systems with a chaotic classical limit. Anti scars lead to a large number of exponentially narrow isolated resonances wh en the single-channel (or tunneling) opening is located on a short unstable orbit of the closed system; the probability to remain in the system at lon g times is thus exponentially enhanced over the random matrix theory predic tion. The distribution of resonance widths and the probability to remain ar e quantitatively given in terms of only the stability matrix of the orbit o n which the opening is placed. The long-time remaining probability density is nontrivially distributed over the available phase space; it can be enhan ced or suppressed near orbits other than the one on which the lead is locat ed, depending on the periods and classical actions of these other orbits. T hese effects of the short periodic orbits on quantum decay rates have no cl assical counterpart, and first appear on times scales much larger than the Heisenberg time of the system. All the predictions are quantitatively compa red with numerical data. [S1063-651X(99)12805-8].