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This study analyzes metastable state decay in the quantum Kramers model under weak-to-intermediate dissipation. It refines calculations for energy loss and escape rates, showing good agreement with simulations.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Metastable state decay is crucial in various physical phenomena.
  • The quantum Kramers model describes decay rates influenced by dissipation.
  • Previous work extended Grabert's perturbative approach to discrete baths.

Purpose of the Study:

  • To analyze metastable state decay within the quantum Kramers model in the weak-to-intermediate dissipation regime.
  • To extend the perturbative approach to continuous bath spectra and derive explicit correction terms.
  • To determine the validity range of the perturbative approach and assess its accuracy.

Main Methods:

  • Extended Grabert's perturbative approach to include second-order terms in classical equations of motion.
  • Accounted for secular terms, reducing equations of motion to a time-dependent frequency (TDF) oscillator.
  • Derived analytic expressions for the characteristic function of energy loss and its cumulants for a cubic potential with Ohmic dissipation.

Main Results:

  • Explicit expressions for fourth-order corrections to linear response theory were obtained.
  • The perturbative approach is valid for γ/ωb < 0.26, including the turnover region.
  • Dominant corrections reduce average energy loss and dispersion by up to ~10% with increasing dissipation.

Conclusions:

  • The developed approach provides accurate corrections to the linear response theory for metastable decay.
  • Calculated corrections to depopulation factors and escape rates show good agreement with numerical simulations for the classical Kramers model.
  • The findings validate the robustness and accuracy of the linear response theory in this regime.