A standard perspective on ghosts

Abstract

Abstract The semiclassical periodic orbit formula is compared with the asymptotic expansion of exact analytical expressions for the trace of unitary propagators in the case of the quantum standard map. The emphasis is on the role played by ‘ghost orbits’, which are periodic orbits in a complex phase space and hence have complex actions. These, as well as the real orbits, are shown to be necessary to recover the usual fixed point quantization in the semiclassical limit. Recent results on (i) ghost orbits arising from different bifurcation schemes; (ii) the role of boundary conditions on the spectral contribution of different orbits, both real and ghost; (iii) scarred wavefunctions supported on ghost orbits; and (iv) the relevance of these complex orbits to the analysis of new experiments in mesoscopic devices are also presented.