Generalized spin mapping for quantum-classical dynamics.

@article{Runeson2020GeneralizedSM,
  title={Generalized spin mapping for quantum-classical dynamics.},
  author={Johan E Runeson and Jeremy O. Richardson},
  journal={The Journal of chemical physics},
  year={2020},
  volume={152 8},
  pages={
          084110
        }
}
We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. E. Runeson and J. O. Richardson, J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system and a spin-1/2 particle. In the present paper, we generalize this method to describe the dynamics of N-level systems. This is done via a mapping to a classical phase space that preserves the SU(N)-symmetry of the original… 

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References

SHOWING 1-10 OF 107 REFERENCES

A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes.

A different classical electronic Hamiltonian for the treatment of electronically nonadiabatic processes is proposed, which maps the dynamics of F coupled electronic states to a set of F spin-(1)/2 degrees of freedom (DOF), similar to the Fermionic spin model described by Miller and White.

Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics.

This paper considers two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical approximation (LSC) approximation.

On the discrete Wigner function for SU(N)

We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and

How quantum is radical pair magnetoreception?

It is found that semiclassical approximations to the spin dynamics of radical pairs only provide a satisfactory description of the anisotropic product yields when there is no electron spin-spin coupling, a situation unlikely to be consistent with a magnetic sensing function.

A new perspective for nonadiabatic dynamics with phase space mapping models.

CMMs demonstrate overall reasonably accurate dynamics behaviors in comparison to exact results even in the asymptotic long time limit for various spin-boson models and site-exciton models, and may lead to practically useful approaches to study nonadiabatic processes in realistic molecular systems in the condensed phase.

Trajectory-adjusted electronic zero point energy in classical Meyer-Miller vibronic dynamics: Symmetrical quasiclassical application to photodissociation.

Examples demonstrate that this slight modification to the standard SQC/MM approach significantly improves treatment of the multistate nonadiabatic dynamics following a Franck-Condon type vertical excitation onto a highly repulsive potential energy surface as is typical in the photodissociation context.

Improved population operators for multi-state nonadiabatic dynamics with the mixed quantum-classical mapping approach.

It is shown that by treating the electronic-state population operator in any system can be exactly rewritten as a sum of a traceless operator and the identity operator, and the accuracy of traditional quasiclassical dynamics methods can be drastically improved, without changes to their underlying equations of motion.

Mixed Quantum-Classical Description of Excitation Energy Transfer in a Model Fenna-Matthews-Olsen Complex

The Fenna−Matthews−Olsen (FMO) complex has recently become a paradigmatic model system in terms of understanding the long-lived electronic quantum coherence that has been experimentally observed in

Quantum mechanics as a statistical theory

  • J. E. Moyal
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1949
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the
...