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Non-Hermitian surface hopping.

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We introduce a generalized non-Hermitian equation of motion (nH-EOM) for improved quantum dynamics simulations. This method enhances trajectory surface hopping by including decoherence and phase shifts, outperforming standard approaches.

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Area of Science:

  • Quantum dynamics
  • Computational chemistry
  • Theoretical physics

Background:

  • Standard trajectory surface hopping methods struggle to accurately model decoherence and phase shifts in quantum systems.
  • The Born-Huang expansion is a foundational framework for describing quantum-classical dynamics.

Purpose of the Study:

  • To develop a generalized non-Hermitian equation of motion (nH-EOM) that overcomes limitations of standard surface hopping dynamics.
  • To incorporate decoherence and phase shift effects into semiclassical simulations.

Main Methods:

  • Derivation of the nH-EOM based on the Born-Huang expansion and polar representation of the nuclear factor.
  • Inclusion of a skew symmetry term (iΓ) for decoherence and a kinetic-energy renormalization term for phase shifts.
  • Efficient numerical solution using a semiclassical approximation within Tully's fewest-switches surface hopping (FSSH) algorithm.

Main Results:

  • The nH-EOM successfully accounts for decoherence and phase shifts without altering representation invariance.
  • Numerical applications to model Hamiltonians show superior performance compared to standard FSSH.
  • Results demonstrate closer agreement with exact quantum mechanical calculations.

Conclusions:

  • The generalized nH-EOM offers a more accurate and robust approach for simulating quantum dynamics.
  • This method provides a significant advancement over existing semiclassical surface hopping techniques.
  • The nH-EOM is a promising tool for studying complex quantum phenomena in various scientific fields.