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Sixth-order factorization of the evolution operator for time-dependent potentials.

G Goldstein1, D Baye

  • 1Physique Quantique, CP165/82, Physique Nucléaire Théorique et Physique Mathématique, C.P. 229, Université Libre de Bruxelles, B-1050 Brussels, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
Summary

This study presents a sixth-order factorization for quantum system evolution operators in time-dependent potentials. Higher accuracy is achieved compared to lower orders, but with increased computational cost.

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Area of Science:

  • Quantum mechanics
  • Theoretical physics
  • Computational physics

Background:

  • Accurate simulation of quantum systems is crucial for understanding their behavior.
  • Time-dependent potentials present challenges for standard quantum evolution calculations.
  • Existing factorization methods have limitations in accuracy and computational efficiency.

Purpose of the Study:

  • To develop and evaluate a higher-order (sixth-order) factorization for the quantum evolution operator.
  • To compare the accuracy and computational cost of the sixth-order method against lower-order approximations.
  • To determine the applicability of the sixth-order method for achieving high-accuracy quantum simulations.

Main Methods:

  • Factorization of the quantum evolution operator using unitary exponential operators.

Related Experiment Videos

  • Application of the time-ordering method for deriving the sixth-order expression.
  • Numerical comparison of the sixth-order method with lower-order factorizations using one-dimensional quantum systems.

    • Main Results:

    • The sixth-order factorization provides improved accuracy for a given time step compared to lower orders.
    • The computational cost per time step significantly increases with the sixth-order approximation.
    • The enhanced accuracy is most beneficial in scenarios demanding high precision.

    Conclusions:

    • The sixth-order factorization offers a more accurate approach to simulating quantum systems in time-dependent potentials.
    • The trade-off between accuracy and computational expense must be considered when selecting the appropriate order of approximation.
    • This method is particularly valuable for high-accuracy quantum dynamics calculations where computational resources permit.