Compare quasiprobability instantons with the Keldysh formulation

Determine how the quasiprobability-based quantum instanton approach compares with the Keldysh path-integral formulation for calculating activation barriers in bosonic systems, particularly with respect to numerical convergence.

Background

The paper finds that numerical convergence depends strongly on the chosen quasiprobability representation and boundary-value solver. In the studied spin models, some representations converge reliably while others fail in parts of parameter space, even when the physical activation barriers are representation-independent.

The authors note that convergence problems have also been reported for Keldysh path-integral calculations of activation barriers in bistable bosonic oscillators. They therefore leave unresolved whether the quasiprobability-based and Keldysh formulations differ in numerical robustness, and whether systematic comparisons can identify representations and algorithms that make instanton calculations more tractable.

References

This raises the question of how, in bosonic systems, our quasiprobability-based approach compares with the Keldysh formulation in terms of numerical convergence.

— Quantum instanton approach to metastable collective spin systems: Numerical implementation and applications  (2610.21684 - Chudak et al., 15 Oct 2026) in Section 6, Conclusions

Identifying conditions under which the SW approach reliably describes observable metastable behavior, or instead misses significant non-Gaussian effects, remains an important open problem.

— Quantum instanton approach to metastable collective spin systems: Numerical implementation and applications  (2610.21684 - Chudak et al., 15 Oct 2026) in Section 6, Conclusions