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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.