Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum.

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.