Wavepackets, periodic orbits and semiclassical quantization.

F. Nicacio, Alfredo Ozorio de Almeida, K. Dechoum +1 more

SongJJ, LiXG

The general quantization condition for periodic orbits in a two-dimensional integrable system is presented via the Berry-Tabor trace formula. Using the quantization and a periodicity condition of periodic orbits the semiclassical quantization condition and semiclassical quantized energies of a two dimensional uncoupled quartic oscillator system are given in detail. The semiclassical quantized energies-periodic orbits correspondence is also analysed.

Robert G. Littlejohn

Jörg Main

Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and to extract dynamical information from quantum spectra which has been unattainable before, such as bifurcations of orbits, the uncovering of hidden ghost orbits in complex phase space, and the direct observation of symmetry breaking effects. The method also solves the fundamental convergence problems in semiclassical periodic orbit theories -- for both the Berry-Tabor formula and Gutzwiller's trace formula -- and can therefore be applied as a novel technique for periodic orbit quantization, i.e., to calculate semiclassical eigenenergies from a finite set of classical periodic orbits. The advantage of periodic orbit quantization by harmonic inversion is the universality and wide applicability of the method, which will be demonstrated in this work for v...

Jonathan M. Robbins

Gábor Vattay, Per E. Rosenqvist

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\ensuremath{\Elzxh}$ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first $\ensuremath{\Elzxh}$ contribution to the exact quantum mechanical results.