1211.5760 (T. Micklitz et al.)

Semiclassical theory of chaotic quantum resonances    [PDF]

T. Micklitz, A. Altland

In semiclassical regimes the resonance spectra of open chaotic quantum systems display universal features generally subsumed under the name fractal Weyl law. Specifically, the density of resonances scales as $\hbar^{-d_f}$ with a fractal dimension $d_f$, and the decay rates show a finite gap of width $\sim t_E^{-1}$, where $t_E$ is the so-called Ehrenfest time. We present a semiclassical theory quantitatively explaining these phenomena. Describing the behavior of resonance states in terms of the phase space evolution of Wigner functions, our theory matches both the classical limit $\hbar=0$, and the deep quantum limit where strongly diffractive scattering governs the decay process.

View original: http://arxiv.org/abs/1211.5760