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Herman-Kluk-like semi-classical initial-value representation for Boltzmann operator.

Binhao Wang1, Fan Yang2, Chen Xu1

  • 1School of Physics, Renmin University of China, Beijing 100872, China.

The Journal of Chemical Physics
|February 9, 2026
PubMed
Summary
This summary is machine-generated.

A new semi-classical method, the Herman-Kluk-like (HK-like) initial-value representation (IVR), accurately calculates the imaginary-time propagator for quantum systems. This approach overcomes high-temperature divergences, enabling broader applications in chemical physics.

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Area of Science:

  • Quantum Mechanics
  • Chemical Physics
  • Computational Chemistry

Background:

  • The Herman-Kluk (HK) initial-value representation (IVR) is a standard method for quantum real-time propagation.
  • The Boltzmann operator is essential for describing thermal properties in quantum systems.
  • Direct transformation of the HK IVR to imaginary time leads to divergences, limiting its use.

Purpose of the Study:

  • To develop a stable and accurate semi-classical initial-value representation (IVR) for the imaginary-time propagator.
  • To address the divergence issue encountered when transforming real-time propagators to imaginary time.
  • To create a method applicable to systems with bounded forces or long-range harmonic potentials.

Main Methods:

  • Developed a Herman-Kluk-like (HK-like) semi-classical IVR for the imaginary-time propagator ⟨x̃|e-Ĥ/(kBT)|x⟩.
  • The method is applicable to systems with finite force intensity or harmonic long-range potentials.
  • The resulting integrand is a real Gaussian function of initial and final positions.

Main Results:

  • The derived HK-like IVR successfully overcomes the high-temperature divergence problem.
  • The method is exact for free particles and harmonic oscillators.
  • Numerical examples demonstrate its effectiveness for other quantum systems.

Conclusions:

  • The new HK-like IVR provides a robust tool for calculating imaginary-time propagators in quantum systems.
  • This method enhances the applicability of semi-classical techniques in chemical dynamics and quantum physics.
  • The real Gaussian integrand simplifies practical implementation for realistic problems.