Emergence of classical-like conductance extremum in a quantum wire with a narrow barrier

This paper investigates the emergence of classical-like behavior within a fundamentally quantum system. Our findings demonstrate that even when quantum phenomena, such as tunneling, are dominant, their collective behavior can yield a macroscopic observable -specifically conductance-that is quantitatively described by classical parameters, notably without the explicit appearance of Planck's constant, h. We show that this “classical-like” domain is not a parameter-specific coincidence but a robust feature that exists near a specific point. Our analysis reveals a striking insensitivity to the precise value of h; quantitatively, a relative change in conductance ΔG/G is found to be less than (Δh/h)², implying a suppressed dependence on h beyond simple linear scaling. This finding challenges conventional paradigms of the quantum-to-classical transition, which typically invoke the limit where h→0, by proposing an alternative mechanism for classical emergence rooted in the collective behavior of quantum effects. Intriguingly, these results predict that the conductance within this “classical-like” regime is consistently approximately 0.75G₀ (where G₀ = 2e²/h), a value that arises when the specific conditions for the emergence of this regime are met. The close proximity of this theoretical value to the long-standing 0.7G₀ anomaly observed in quantum point contacts hints at a potential intrinsic connection. Investigating this relationship may offer new avenues for understanding the origins of this puzzle and providing deeper insights into the complex interplay between quantum coherence, interactions, and classical phenomenology in mesoscopic systems.