Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian.

Area of Science:

• Quantum mechanics
• Molecular spectroscopy
• Chemical physics

Background:

• High-resolution IR spectra of polyatomic molecules show peak splittings (0.01-0.1 cm(-1)).
• Dynamical tunneling is a quantum mechanism for energy flow across phase-space barriers.
• Arnol'd diffusion is a classical mechanism involving resonance networks (Arnol'd web) for phase-space energy flow.

Purpose of the Study:

• Investigate the nature of observed spectral peak splittings.
• Compare the roles of dynamical tunneling and Arnol'd diffusion in energy flow.
• Explore a non-convex Hamiltonian relevant to molecular systems.

Main Methods:

• Analysis of a non-convex Hamiltonian that deviates from Nekhoroshev theorem conditions.
• Theoretical comparison of dynamical tunneling and Arnol'd diffusion rates.
• Examination of energy flow in the nearly integrable regime.

Main Results:

• Dynamical tunneling dominates over fast Arnol'd diffusion in the nearly integrable regime for non-convex Hamiltonians.
• A novel form of dynamical tunneling is identified.
• The study clarifies the mechanism behind spectral peak splittings.

Conclusions:

• Dynamical tunneling is the primary cause of observed spectral peak splittings in polyatomic molecules.
• The findings highlight the importance of quantum effects in molecular dynamics.
• A new type of dynamical tunneling expands our understanding of quantum phenomena.