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Calculating expectations with time-dependent perturbations in quantum Monte Carlo.

M H Kalos1, F Arias de Saavedra

  • 1Lawrence Livermore National Laboratory, Livermore, California 94550, USA.

The Journal of Chemical Physics
|September 9, 2004
PubMed
Summary

A novel quantum diffusion Monte Carlo method uses imaginary time perturbations to calculate expectation values for operators that do not commute with the Hamiltonian. This approach is validated for the harmonic oscillator and helium atom.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Quantum chemistry

Background:

  • Calculating expectation values of operators that do not commute with the Hamiltonian in quantum systems is challenging.
  • The quantum diffusion Monte Carlo (QDMC) method is a powerful tool for simulating quantum systems.
  • Existing QDMC methods have limitations in handling non-commuting operators.

Purpose of the Study:

  • To introduce a new method for computing expectation values of nondifferential operators within QDMC.
  • To extend the applicability of QDMC to a broader range of quantum mechanical problems.
  • To demonstrate the effectiveness of the proposed technique.

Main Methods:

  • A small perturbation, periodic in imaginary time, is introduced into the QDMC framework.

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  • This perturbation allows for the computation of expectation values of operators that do not commute with the Hamiltonian.
  • The method is applied to standard quantum mechanical models.

    • Main Results:

    • The proposed method successfully computes expectation values for operators that do not commute with the Hamiltonian.
    • Validation was performed using the harmonic oscillator model.
    • Further validation was conducted using the helium atom, confirming the method's accuracy.

    Conclusions:

    • The developed imaginary time perturbation method is a valid and effective extension of QDMC.
    • This technique enhances the capability of QDMC for complex quantum system simulations.
    • The approach offers a robust way to handle non-commuting operators in quantum Monte Carlo simulations.