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Trotter-based simulation of quantum-classical dynamics.

Dónal Mac Kernan1, Giovanni Ciccotti, Raymond Kapral

  • 1School of Physics, Trinity College Dublin, Dublin 2 and School of Physics, University College Dublin, Dublin 4, Ireland.

The Journal of Physical Chemistry. B
|December 25, 2007
PubMed
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This study presents a new algorithm for simulating quantum-classical Liouville dynamics, offering a more efficient surface-hopping approach for quantum rate processes in condensed phases.

Area of Science:

  • Quantum dynamics
  • Condensed matter physics
  • Theoretical chemistry

Background:

  • Simulating quantum rate processes in condensed phases requires combining quantum and classical dynamics.
  • Existing methods face challenges in accurately and efficiently describing these complex systems.

Purpose of the Study:

  • To develop and present a novel algorithm for simulating the quantum-classical Liouville equation.
  • To provide an efficient surface-hopping representation of quantum dynamics in condensed phase systems.

Main Methods:

  • The algorithm employs a Trotter decomposition of the quantum-classical propagator.
  • Monte Carlo sampling of quantum transitions is used to generate a surface-hopping representation.
  • A novel expression for the nonadiabatic propagator is derived for efficient Monte Carlo sampling and exact energy conservation.

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Main Results:

  • The developed algorithm accurately reproduces exact quantum results for the spin-boson model.
  • It demonstrates superior performance compared to other schemes, requiring fewer trajectories for stronger nonadiabatic coupling and longer simulation times.
  • The method exactly conserves total energy within individual trajectories.

Conclusions:

  • The presented algorithm offers an efficient and accurate method for simulating quantum-classical dynamics.
  • This approach advances the study of quantum rate processes in condensed phase systems.
  • The surface-hopping representation provides a robust framework for future theoretical investigations.