The effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
The effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by two coupled quartic oscillators, which on the classical level exhibits mixed phase space dynamics. We show that the signature of a pitchfork bifurcation …