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Mixed Quantum-Classical Dynamics under Arbitrary Unitary Basis Transformations.

Ken Miyazaki1, Alex Krotz1, Roel Tempelaar1

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This study introduces a novel method for mixed quantum-classical dynamics, enabling arbitrary basis transformations for both quantum and classical coordinates. This approach efficiently captures complex dynamics using reduced basis sets, lowering computational costs.

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Area of Science:

  • Quantum mechanics and computational chemistry
  • Development of advanced simulation methodologies

Background:

  • Minimizing computational cost in quantum calculations often involves basis set truncation.
  • Existing mixed quantum-classical methods are limited by their fixed basis representations.

Purpose of the Study:

  • To develop a flexible mixed quantum-classical dynamics framework adaptable to arbitrary basis sets.
  • To enable efficient simulations of quantum systems by allowing optimal basis truncation.

Main Methods:

  • Derivation of classical equations of motion under unitary transformations.
  • Integration of these transformed equations into mixed quantum-classical dynamics.
  • Utilizing complex-valued coordinates for classical degrees of freedom.
  • Application to surface hopping calculations of electronic scattering with phonons.

Main Results:

  • Demonstrated successful application of unitary transformations to classical dynamics.
  • Showcased the ability to use arbitrary bases for both quantum and classical parts.
  • Achieved faithful dynamics simulation with significantly reduced classical and quantum basis sets.
  • Successfully modeled electronic carrier scattering on an impurity in the presence of phonons.

Conclusions:

  • The proposed method significantly enhances the efficiency of mixed quantum-classical simulations.
  • Unitary transformations offer a powerful tool for optimizing basis sets in quantum dynamics.
  • This approach provides a flexible and computationally advantageous alternative for studying complex quantum phenomena.