On the short-time behaviour of quantum unstable systems

Jacob Levitan

Lev Kaplan

We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behaviour of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics framework leads to predictions about statistical long-time and stationary properties of quantum systems with chaotic classical analogues. Many long-time quantum properties can be quantitatively understood using only short-time classical dynamics information; these include wavefunction intensity distributions, intensity correlations in phase space and correlations between wavefunctions, and distributions of decay rates and conductance peaks in weakly open systems. Strong deviations from random matrix theory are predicted and observed in the presence of short unstable periodic orbits.

Teresa Fonseca, Paolo Grigolini A, Paolo Marin

W. Garczyński

Marek Nowakowski, N. G. Kelkar, George Rupp +4 more

Whereas the short time behaviour of an unstable quantum mechanical system is well understood from its theoretical as well as experimental side, the long time tail of the very same systems has neither been measured experimentally nor is there a theoretical agreement on how to handle it. We suggest a possible way out of this unsatisfactory state of art. Theoretically we suggest that the correct spectral function entering the Fock‐Krylov method to calculate the survival amplitude is proportional to the density of states of a resonance. The latter is essentially the energy derivative of a phase shift. As a bonus, we can connect the survival probability to scattering data via the phase shift. The method then not only establishes the spectral function, but is per se a semi‐empirical method to extract the large time behaviour from scattering data.

Aizar Enciso Domínguez, Piotr Kielanowski