Decay Rates of Metastable States in Cubic Potential by Variational Perturbation Theory

Abstract

Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues obtained from a WKB expansion; for low barriers, the variational resummation procedure converts the non-Borel-summable Rayleigh-Schrö\-din\-ger expansion into an exponentially fast convergent one. The results in the two regimes match and yield very accurate imaginary parts of the energy eigenvalues. This is demonstrated by comparison with the complex eigenvalues from solutions of the Schrödinger equation via the complex-coordinate rotation method.

Cited by in corpus (7)

• Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian
• Resonant Nucleation
• Bubbling the False Vacuum Away
• A resurgence analysis for cubic and quartic anharmonic potentials
• Observing Quantum Tunneling in Perturbation Series
• Damped collective motion of many body systems: A variational approach to the quantal decay rate
• Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams