Persistence of QCLE-induced negativities in high-dimensional classical environments

Determine whether the mixed quantum–classical Liouville equation (QCLE) continues to produce forbidden negativities in joint classical phase-space probabilities (for position or momentum) and in their marginal densities as the number of classical bath degrees of freedom increases, i.e., ascertain if such violations persist or vanish in progressively higher-dimensional surroundings.

Background

The paper demonstrates that QCLE evolution can violate positivity in marginal phase-space densities for low-dimensional benchmark models, even when reduced observables (such as populations) agree with exact quantum dynamics. A negativity index is introduced to quantify these violations and is shown to diminish as the initial energy increases relative to subsystem gaps.

While the authors argue that, in realistic condensed-phase systems, negative pseudo-density regions may occupy an exponentially small fraction of the classical phase-space volume, they explicitly note that it remains unresolved whether such forbidden negativities—either in joint probabilities or marginals—actually persist as the number of classical degrees of freedom grows. This question addresses the scalability and physical relevance of the observed pathologies in higher-dimensional baths.