Late-time decay of the would-be ground state

Determine whether the would-be ground state of the coupled normal–ghost oscillator system eventually undergoes genuine decay at exponentially large times, despite the numerically observed nonzero, oscillatory survival probability over accessible time intervals.

Background

For small and moderate couplings, the numerical survival probability of the would-be ground state remains nonzero and exhibits residual oscillations. The computations, however, are reliable only up to finite times because increasing the ultraviolet cutoff rapidly increases the computational cost.

Consequently, the observed protection against decay establishes long-lived metastability rather than absolute stability. The authors explicitly leave unresolved whether the oscillations persist indefinitely or eventually give way to complete decay.