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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
1Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
The Journal of Chemical Physics
|October 16, 2025
Summary
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.
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.
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