Quantum

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

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 27/10/2026, 04:13:25 UTC.

Briefings

A 2026 arXiv preprint establishes that higher-order squeezing Hamiltonians have self-adjoint extensions where classical trajectories reach infinity in finite time. The study relates these quantum extensions via boundary amplitudes and semiclassical coherent state propagation, using discrete Fourier transforms to derive ray matrices. It finds that after the first passage through infinity, the Husimi probability measure converges to point masses on classical branches, with weights equal to the squared moduli of the matrix entries. For positive energy, the limit after any fixed number of passages is determined by powers of the unitary ray matrix, not iterations of its squared-modulus matrix. The research also realizes these limits using concentrated complex amplitudes for an energy-preserving Liouville extension, distinguishing deterministic classical gluings from coherent boundary mixing.

Key points

• Higher-order squeezing Hamiltonians have self-adjoint realizations where classical trajectories reach infinity in finite time.
• The proof combines finite-order approximate tail solutions satisfying exact extension boundary conditions with full-norm Gaussian matching and a square-summable residual estimate.

Context

This research addresses the mathematical challenge of defining higher-order squeezing Hamiltonians, which are known to have classical trajectories extending to infinity in finite time. The study provides a rigorous framework relating quantum extensions through boundary amplitudes and semiclassical propagation, offering a new perspective on how quantum systems behave at extreme energy scales.

Limitations

The evidence is an arXiv preprint (arXiv:2610.33378v1) from October 2026, meaning it represents unverified research. The analysis covers only the specific case of positive energy systems and does not address negative energy regimes or other physical contexts. The convergence of the Husimi measure to point masses is a theoretical result based on the provided proof, not confirmed experimental data.

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