Quantum electromechanical L designs with discrete charge: Second harmonic (2qe/h2qe/h) in the persistent current

A simple model of a purely inductive continuously deformed quantum circuit with charge discreteness is introduced. Without deformations, the persistent current is periodic in the pseudoflux variable (frequency qeh). Spatial dynamic deformations in the geometry are modeled as a mechanical harmonic oscillator (U(x)∼x2U(x)∼x2). As consequence of the electromechanical interaction there are important corrections to the electrical current crossing the inductance (persistent current). At first order, a generation of a second harmonic (ω=2qeh) appears. For non-harmonic mechanical systems (U(x)∼x2nU(x)∼x2n, n>1n>1) we conjecture the generation of multiple modes.