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A bosonic perspective on the classical mapping of fermionic quantum dynamics.

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The Meyer-Miller (MM) Hamiltonian accurately maps fermionic quantum dynamics to classical equations. This classical approach captures essential quantum effects like interference, even for interacting systems.

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Area of Science:

  • Quantum dynamics
  • Computational chemistry
  • Theoretical physics

Background:

  • Fermionic quantum dynamics are complex to simulate classically.
  • Classical mappings offer a computationally efficient alternative.
  • The Meyer-Miller (MM) Hamiltonian is a known classical mapping method.

Purpose of the Study:

  • To evaluate the Meyer-Miller (MM) Hamiltonian for mapping fermionic quantum dynamics.
  • To compare MM with other fermionic mapping techniques like spin mapping and Li-Miller mapping (LMM).
  • To assess the accuracy of classical mappings in capturing quantum phenomena.

Main Methods:

  • Application of the original Meyer-Miller (MM) Hamiltonian.
  • Comparison with spin mapping (with and without Jordan-Wigner transformation) and Li-Miller mapping (LMM).
  • Analysis of non-interacting and interacting fermionic systems, including impurity models and excitonic energy transfer models.

Main Results:

  • The MM mapping provides exact one-body density dynamics for non-interacting fermions.
  • Including fermionic anti-symmetry (Jordan-Wigner transform) did not improve, and worsened, classical description for non-interacting systems.
  • MM and LMM showed similar performance for interacting models, with MM sometimes outperforming LMM compared to quantum results.
  • Classical mappings successfully captured interference effects in energy transfer models.

Conclusions:

  • The Meyer-Miller (MM) Hamiltonian is a viable and effective method for classical mapping of fermionic quantum dynamics.
  • Classical mappings, including MM and LMM, can accurately describe complex quantum phenomena like interference.
  • The MM mapping offers a promising computationally efficient approach for studying fermionic systems.