Fractional squeezing: spectra and dynamics from generalized squeezing Hamiltonian with fractional orders

We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately predict the behaviour at these critical points, which are challenging for conventional computational methods. Based on our numerical calculations, we identify with a high degree of confidence the point at which the spectrum turns from continuous to discrete and the point at which oscillations turn from having asymptotically infinite amplitudes to finite amplitudes. Furthermore, we numerically investigate the behaviour in the large $n$ regime and provide an intuitive explanation that coincides with the numerical results.