False Vacuum Decay across the Quantum-to-Thermal Crossover: A Comparison of Real-Time Observables

We develop a real-time Wigner-functional lattice framework with positive Hartree-Gaussian initial sampling and introduce a connected-cluster survival criterion for extracting false-vacuum decay rates across the crossover from quantum fluctuations to thermal nucleation. At high temperatures, the connected-cluster rate agrees well with the Hartree-resummed thermal nucleation benchmark, while the commonly used global-survival criterion can give substantially smaller rates because of multi-seed dynamics and global averaging. At low temperatures, the connected-cluster and global-survival rates approach each other in the dilute-event regime, whereas the false-vacuum fraction observable can be contaminated by transient spatial conversion and kink-antikink reflection. Our results clarify how different real-time observables encode distinct aspects of metastable decay.