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Refined approach to cellularization: Going from Heller's thawed Gaussian approximation to Herman-Kluk's initial value

Sergey V Antipov1, Fabian Kröninger1, Jiří J L Vaníček1

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A new cellularization scheme refines the Herman-Kluk propagator for semiclassical simulations. This method improves phase space sampling and offers convergence to established approximations, enhancing quantum dynamics calculations.

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Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • The Herman-Kluk propagator is a key tool in semiclassical methods for simulating quantum dynamics.
  • Standard cellularization techniques can face limitations in accurately sampling phase space.
  • The dephasing representation has previously utilized related filtering techniques.

Purpose of the Study:

  • To introduce a refined cellularization scheme for the Herman-Kluk propagator.
  • To improve the efficiency and accuracy of semiclassical quantum dynamics simulations.
  • To establish convergence properties with respect to trajectory number.

Main Methods:

  • Implementation of an inverse Weierstrass transform for cellularization.
  • Optimal scaling of cell size based on the number of cells.
  • Correlation of sampling density with cell size for effective phase space coverage.
  • Calculation of autocorrelation functions and spectra for model systems.

Main Results:

  • The refined scheme effectively samples the phase space of the initial system state.
  • Demonstrated convergence to the original Herman-Kluk result with infinite trajectories.
  • Showed convergence to the thawed Gaussian approximation with a single trajectory.
  • Successfully calculated autocorrelation functions and spectra for both integrable and chaotic systems.

Conclusions:

  • The refined cellularization scheme offers an improved approach for semiclassical simulations.
  • This method provides a bridge between different semiclassical approximations.
  • The technique is validated by its performance on diverse model systems, highlighting its broad applicability in quantum dynamics.