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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Deriving the exact nonadiabatic quantum propagator in the mapping variable representation.

Timothy J H Hele1, Nandini Ananth1

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA. ananth@cornell.edu.

Faraday Discussions
|October 19, 2016
PubMed
Summary

This study introduces an exact quantum propagator for nonadiabatic dynamics using mapping variables. This method enables efficient classical-like modeling of complex quantum systems and reaction rates.

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Area of Science:

  • Quantum dynamics
  • Chemical physics
  • Theoretical chemistry

Background:

  • Modeling nonadiabatic dynamics in multi-state systems is computationally challenging.
  • Existing methods often involve approximations that limit accuracy or scalability.

Purpose of the Study:

  • To derive an exact quantum propagator for nonadiabatic dynamics.
  • To establish a theoretical foundation for accurate and efficient classical-like dynamics.

Main Methods:

  • Utilizing the mapping variable representation for nuclear and electronic degrees of freedom.
  • Developing a Moyal series expansion of the Liouvillian.
  • Combining imaginary-time path-integral with the exact Liouvillian.

Main Results:

  • An exact quantum propagator for multi-state nonadiabatic dynamics was derived.
  • Approximations of the exact Liouvillian yield known semiclassical and mixed quantum-classical methods.
  • Analytic expressions for thermal quantum real-time correlation functions were obtained.

Conclusions:

  • The derived method provides a rigorous framework for classical-like dynamics.
  • This approach facilitates accurate computation of observables like electron transfer rates.
  • It offers a pathway to efficiently model large, complex quantum systems.