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This study introduces a novel semiclassical method for time-dependent barrier tunneling using only real-valued trajectories. This approach simplifies calculations and yields accurate transmission probabilities, aligning well with quantum mechanics.

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Area of Science:

  • Quantum Mechanics
  • Computational Physics
  • Chemical Physics

Background:

  • Time-independent semiclassical treatments of barrier tunneling are well-established.
  • Existing time-dependent semiclassical methods often rely on complex-valued trajectories, introducing significant computational challenges.

Purpose of the Study:

  • To develop a new semiclassical method for time-dependent barrier tunneling that utilizes only real-valued trajectories.
  • To avoid the complexities associated with complex-valued trajectories in semiclassical tunneling calculations.

Main Methods:

  • The time-dependent wave packet is expressed as an integration over momentum.
  • The action function is expanded to second order around a specific momentum value.
  • A "pseudo-stationary phase" approximation is employed, differing from the standard stationary phase approximation.

Main Results:

  • The method successfully employs real-valued trajectories and real initial momentum.
  • Calculated transmission probabilities show good agreement with exact quantum mechanical results.
  • The approach simplifies the treatment of time-dependent tunneling through potential barriers.

Conclusions:

  • The presented pseudo-stationary phase approximation offers a computationally tractable and accurate method for time-dependent barrier tunneling.
  • This real-valued trajectory approach provides a valuable alternative to methods using complex trajectories.
  • The findings have implications for various fields requiring accurate quantum tunneling simulations.