Precise variational tunneling rates for anharmonic oscillator with g<0

TL;DR

This paper enhances variational methods to accurately compute tunneling rates in anharmonic oscillators with negative coupling, achieving high precision and validating results against complex rotation techniques.

Contribution

It introduces an improved variational approach for calculating tunneling rates in anharmonic oscillators with g<0, providing highly accurate results and a novel validation method.

Findings

Achieved relative error less than 10^{-5} in perturbation coefficients

Derived all perturbation coefficients from the imaginary part of the energy

Validated results against complex rotation method

Abstract

We systematically improve the recent variational calculation of the imaginary part of the ground state energy of the quartic anharmonic oscillator. The results are extremely accurate as demonstrated by deriving, from the calculated imaginary part, all perturbation coefficients via a dispersion relation and reproducing the exact values with a relative error of less than $10^{-5}$. A comparison is also made with results of a Schr\"{o}dinger calculation based on the complex rotation method.