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Spectroscopic response theory with classical mapping Hamiltonians.

Kritanjan Polley1, Roger F Loring1

  • 1Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA.

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|December 2, 2020
PubMed
Summary
This summary is machine-generated.

This study extends the classical Meyer-Miller-Stock-Thoss mapping Hamiltonian to compute quantum response functions from classical dynamics. This approach enables new semiclassical approximations for spectroscopic observables, particularly for systems with classical nuclear degrees of freedom.

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Area of Science:

  • Quantum dynamics
  • Chemical physics
  • Spectroscopy

Background:

  • Exact quantum dynamics with time-independent Hamiltonians can be simulated using classical mechanics via the Meyer-Miller-Stock-Thoss mapping Hamiltonian.
  • Extending this to time-dependent Hamiltonians, particularly those arising from classical fields, is crucial for computing quantum response functions.

Purpose of the Study:

  • To generalize the Meyer-Miller-Stock-Thoss mapping Hamiltonian to include time-dependence from classical fields.
  • To develop a theoretical framework for computing quantum response functions from classical dynamics.
  • To establish a foundation for novel semiclassical approximations in spectroscopy.

Main Methods:

  • Generalization of the mapping Hamiltonian to incorporate time-dependence.
  • Development of classical analogues of quantum density operator diagrams.
  • Application of two semiclassical approaches to calculate temperature-dependent two-dimensional electronic spectra.

Main Results:

  • Established the equivalence between quantum response theory and classical response theory using the mapping Hamiltonian.
  • Generated classical versions of two-sided quantum density operator diagrams.
  • Demonstrated the utility of the developed semiclassical methods through calculations on an exciton dimer.

Conclusions:

  • The generalized mapping Hamiltonian provides a robust framework for semiclassical calculations of quantum response functions.
  • This work lays the groundwork for advanced semiclassical approximations in spectroscopic analysis.
  • The developed methods offer a computationally tractable alternative for studying complex quantum systems.