Symplectic Constraints in Quantum Reaction Dynamics: Squeezed-State Suppression and Candidate Width Scales

• URL: http://arxiv.org/abs/2604.10625v1
• Date: Sun, 12 Apr 2026 13:02:45 GMT
• Title: Symplectic Constraints in Quantum Reaction Dynamics: Squeezed-State Suppression and Candidate Width Scales
• Abstract summary: We analyze how transverse bath-mode squeezing modifies transmission across a quantum normal-form (QNF) bottleneck.<n>Results reveal a pronounced squeeze-induced suppression of transmission.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical reaction dynamics suggests transport through an index-1 saddle is organized not just by flux, but by local symplectic width scales of bounded proxy neighborhoods near the bottleneck. We investigate if a related geometric effect appears in the quantum regime for highly squeezed Gaussian wavepackets. Building on de Gosson's symplectic approach, we analyze how transverse bath-mode squeezing modifies transmission across a quantum normal-form (QNF) bottleneck. To avoid the instability of propagating states with extreme phase-space eccentricity, we use the Weyl-symbol formulation of the QNF. For the quadratic saddle-center model, we derive an exact baseline transmission formula by convolving the bath's squeezed-state number distribution with the 1D Kemble transmission factor. For anharmonic truncated QNF models, we enforce strict algebraic energy conservation and evaluate exact Gaussian expectation-value diagnostics of the Weyl symbol via Wick-Isserlis moment formulas. Results reveal a pronounced squeeze-induced suppression of transmission. As the squeezed state's bath-plane geometric scale grows relative to the classical candidate width, the expected bath action grows rapidly. Consequently, effective reactive energy is strongly depleted, driving transmission into a severely suppressed regime. We interpret this as evidence of a quantum geometric suppression mechanism consistent with the classical candidate symplectic-width picture. While not yet a rigorous quantum non-squeezing theorem, this work provides a concrete framework linking squeezed-state covariance geometry, normal-form action scales, and mode-specific quantum reactivity near an index-1 saddle.

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