Shape-Controlled Current Asymmetry: The Interplay of Classical and Quantum Forces

A quantum shape effect is investigated in a scattering region containing a movable obstacle, whose vertical position acts as a geometric control dial for quantum transport. Shifting the obstacle reweights the outgoing currents in the upper and lower branches, generating two distinct forces: one of classical and one of quantum origin. The classical component arises from pressure imbalance due to geometric asymmetry, while the quantum contribution stems from confinement-induced spectral reorganization, an analog of the Casimir effect for matter waves. The leading response is found to be linear in the displacement. Results are presented for both two- and three-dimensional geometries, revealing how the interplay between these forces leads to transport imbalance. We further analyze the dependence of the net force on temperature, particle density, and system size, and introduce a shape susceptibility to quantify the system's thermodynamic and transport response to geometric changes. Together, these elements establish a framework linking geometry to current imbalance and point toward shape-controlled routing in future quantum devices.