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Quantum and classical dynamics comparison: A way for selecting the vector potential across diverse frames.

Maryam Pakpour1,2, Amir H Darooneh1, Mohammad Mahmoudi1

  • 1Department of Physics, University of Zanjan, University Blvd., 45371-38791, Zanjan, Iran.

Heliyon
|January 1, 2026
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Summary
This summary is machine-generated.

This study reveals that quantum paths match classical trajectories in intense laser fields only for specific vector potentials. This work offers a new method for selecting the correct laboratory frame vector potential.

Keywords:
Gauge transformationIntense laser fieldKrammers-Henneberger transformation

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Area of Science:

  • Quantum Dynamics
  • Strong-Field Physics
  • Atomic and Molecular Physics

Background:

  • Understanding electron behavior under intense laser fields is crucial for attosecond science and high-harmonic generation.
  • The dipole approximation is commonly used but limits accuracy for strong fields and short distances.
  • Gauge choices and approximations significantly impact theoretical descriptions of quantum systems.

Purpose of the Study:

  • To explore the quantum dynamics of a free electron in an intense laser field.
  • To investigate the validity of the dipole approximation and explore beyond it.
  • To compute quantum paths using the Ehrenfest theorem and compare them with classical trajectories across different gauges.

Main Methods:

  • Systematic computation of quantum paths based on the Ehrenfest theorem.
  • Analysis of electron dynamics considering various gauges (e.g., Coulomb gauge, transverse gauge).
  • Comparison of quantum paths with classical trajectories in both laboratory and moving frames.

Main Results:

  • The quantum path aligns with the classical trajectory in the laboratory frame only for a specific vector potential.
  • Quantum paths derived from alternative gauges show agreement with classical trajectories in their respective moving frames.
  • A novel method for selecting the appropriate vector potential in the laboratory frame is introduced.

Conclusions:

  • Gauge dependence and the choice of vector potential are critical for accurate descriptions of electron dynamics in intense laser fields.
  • The study provides a framework for understanding the relationship between quantum and classical descriptions across different reference frames.
  • This work offers a new perspective on selecting appropriate theoretical frameworks for strong-field phenomena.