Version 4.0 public record for “A Nuisance-Aware Residual-Test Framework for Geometry-Induced Quantum Potentials in Curved Constrained Platforms”. Version 4.0 is a substantive revision of the public record. It updates the title and scientific framing, clarifies the established Jensen–Koppe–da Costa geometric-potential anchor versus the new nuisance-aware residual-test methodology, adds an explicit finite-width/disorder/spin-orbit/electrostatic validity envelope, strengthens the minimum experimental-design protocol, improves figure readability, and synchronizes the journal and Zenodo packages. The work is framed as a conservative methodological and design-level residual-test framework for geometry-induced quantum potentials in curved constrained platforms. The manuscript is anchored to the established Jensen–Koppe–da Costa geometry-induced potential for scalar particles constrained to smooth curves. The standard constrained-curve prediction is represented by the fixed coefficient −1/4, while the residual parameter delta-lambda is defined as a falsifiable null-test quantity. Standard constrained quantum mechanics predicts delta-lambda = 0. The manuscript emphasizes that any nonzero residual should first be treated as a platform anomaly unless it survives curvature scaling, nuisance projection, matched-reference controls, blind residual extraction, and cross-geometry replication. No experimental detection is claimed. The included simulations and prospective bounds remain design-level estimates. The package contains the manuscript, supplementary information, figures, reproducibility code, generated CSV/JSON data, metadata files, and public technical materials sufficient to regenerate the numerical validation tables, platform-specific energy-scale estimates, residual sensitivity plots, and figures.
The quantum first-detection problem concerns the statistics of the time at which a system, subject to repeated measurements, is observed in a prescribed target state for the first time. Unlike its classical counterpart, the measurement back action intrinsic to quantum mechanics may profoundly alter the system dynamics. Here we show that it induces a distinct change in the statistics of the first-detection time. For a quantum particle in one spatial dimension subject to stroboscopic measurements, we observe an algebraic decay of the probability of the first-detection time if the particle is free, an exponential decay in the presence of a confining potential, and a time-dependent crossover between these behaviors if the particle is partially confined. This crossover reflects the purely quantum nature of the detection process, which fundamentally distinguishes it from the first-passage problem in classical systems.
The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum Gibbs states, which are quantum statistical equilibria with prescribed particle, current, and energy densities at each point of space (here R d , d
≥ 1). They assume that such local Gibbs states exist, and show that if the quantum system is initially in a local Gibbs state, then the system stays, in an appropriate asymptotic limit, in a Gibbs state with particle, current, and energy densities now solutions to the Euler equations. Our main contribution in this work is to prove that such local quantum Gibbs states can be constructed from prescribed densities under mild hypotheses, in both the fermionic and bosonic cases. The problem consists in minimizing the von Neumann entropy in the quantum grand canonical picture under constraints of local particle, current, and energy densities. The main mathematical difficulty is the lack of compactness of the minimizing sequences to pass to the limit in the constraints. The issue is solved by defining auxiliary constrained optimization problems, and by using some monotonicity properties of equilibrium entropies.