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Coherent classical-path description of deep tunneling.

Dong H Zhang1, Eli Pollak

  • 1Center for Theoretical and Computational Chemistry and State Key Laboratory of Chemical Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, People's Republic of China 116023.

Physical Review Letters
|November 5, 2004
PubMed
Summary

Classical trajectories can accurately describe deep quantum tunneling. This study introduces "coherent classical paths" to explain this phenomenon, using a novel semiclassical propagator for quantum mechanics.

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Area of Science:

  • Quantum mechanics
  • Physical chemistry
  • Computational chemistry

Background:

  • Deep quantum tunneling presents a significant challenge to semiclassical approximations in quantum mechanics.
  • Accurately modeling tunneling is crucial for understanding chemical reactions and molecular dynamics.

Purpose of the Study:

  • To demonstrate that real-time classical trajectories can accurately describe deep quantum tunneling.
  • To introduce and utilize a novel semiclassical method for calculating quantum propagators.

Main Methods:

  • Employed a recently formulated semiclassical initial value representation series for the quantum propagator.
  • Utilized a prefactor-free semiclassical propagator.
  • Defined and analyzed "coherent classical paths" composed of discontinuous classical trajectories.

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Main Results:

  • Real-time classical trajectories were shown to be sufficient for accurately accounting for deep quantum tunneling.
  • Coherent classical paths, formed by connected classical trajectories, were identified as the mechanism for deep tunneling.
  • The method was applied to analyze thermal and energy-dependent tunneling through a symmetric Eckart barrier.

Conclusions:

  • Semiclassical methods using classical trajectories can effectively model deep quantum tunneling phenomena.
  • The concept of coherent classical paths provides a new framework for understanding tunneling in quantum systems.
  • This approach offers a computationally tractable method for studying quantum tunneling in various chemical and physical systems.