A quantum-classical correspondence in the dynamics around higher order saddle points: a Bohmian perspective

The quantum-classical correspondence in a model four-well potential, exhibiting both first- and second-order saddle points, is analyzed based on Bohm-inspired quantum trajectories whereas the corresponding classical dynamics have been analyzed based on Hamilton's Equations of Motion. The results indicate that there exists some qualitative correspondence between quantum and classical phase-space dynamics in the intermediate energy regimes. However, at both low and very high energy regimes, the quantum trajectories explore classically forbidden regions in the phase-space. The quantum trajectories attain more ergodic properties than their classical counterparts, particularly at the initial stages of the dynamics, as evidenced by their concerned Lyapunov exponents as well as concerned power spectra of the trajectories. Possible implications of the present simulation study in the context of a model isomerization reaction are also discussed. In the quantum domain, the mechanism for the model isomerization reaction (considered herein) could at best be described as a mixture of concerted and sequential mechanism.

Automated summary

Based on Bohm-inspired quantum trajectories, the correspondence between quantum and classical phase-space dynamics in a model four-well potential is analyzed. It is found that there is a qualitative correspondence in the intermediate energy regimes, but quantum trajectories explore classically forbidden regions at both low and high energy regimes. The quantum trajectories exhibit more ergodic properties than classical ones, especially at the initial stages of the dynamics, as indicated by their Lyapunov exponents and power spectra.