Semiclassical dynamics of higher-order squeezing: self-adjoint extensions and coherent returns

arXiv:2610.33378v1 Announce Type: new Abstract: Higher-order squeezing Hamiltonians have several self-adjoint realizations, while their classical trajectories reach infinity in finite time. We relate these extension problems through boundary amplitudes and the semiclassical propagation of coherent states. A discrete Fourier transformation gives the sink-to-source ray matrix of each quantum realization. After the first passage through infinity, the full Husimi probability measure converges to point masses on outgoing classical branches, with weights equal to the squared moduli of the matrix entries. The proof combines finite-order approximate tail solutions satisfying the exact extension boundary condition with full-norm Gaussian matching and a square-summable residual estimate.