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Complex trajectories in chaotic dynamical tunneling.

D G Levkov1, A G Panin, S M Sibiryakov

  • 1Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow 117312, Russia. levkov@ms2.inr.ac.ru

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
PubMed
Summary
This summary is machine-generated.

We developed a new numerical method to study chaotic dynamical tunneling. This technique identifies optimal tunneling pathways, showing good agreement with exact quantum computations.

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Area of Science:

  • Quantum Mechanics
  • Chemical Physics
  • Dynamical Systems Theory

Background:

  • Chaotic dynamical tunneling is a complex quantum phenomenon.
  • Understanding tunneling trajectories in chaotic systems is challenging.
  • Existing methods lack systematic approaches for identifying optimal paths.

Purpose of the Study:

  • To develop a systematic numerical technique for obtaining complex tunneling trajectories.
  • To introduce a heuristic procedure for selecting the least suppressed trajectory.
  • To apply and validate the method in a two-degree-of-freedom quantum mechanical model.

Main Methods:

  • Semiclassical method of complex trajectories.
  • Gradual deformation of classical trajectories to obtain complex paths.
  • Heuristic sorting of trajectories based on suppression exponent.

Main Results:

  • A systematic classification of tunneling solutions was achieved.
  • A fractal structure of unstable classical solutions was inherited by complex trajectories.
  • The phenomenon of optimal tunneling was identified, with a local minimum in the suppression exponent at a specific energy.
  • Semiclassical results showed good agreement with exact quantum computations.

Conclusions:

  • The developed semiclassical method provides a powerful tool for analyzing chaotic dynamical tunneling.
  • The fractal structure of classical solutions plays a crucial role in semiclassical analysis.
  • The concept of optimal tunneling energy offers new insights into quantum transport phenomena.