DEFORMABLE QUANTUM INDUCTANCE (RING) INTERACTING WITH A PHONON FIELD: PERSISTENT ELECTRICAL CURRENTS RE-VISITED ((q_e/ℏ) VERSUS (2q_e/ℏ))

Abstract

The Hamiltonian of a flexible purely inductive quantum circuits, with discrete charge (q e ), coupled to the vibrational degrees of a lattice (phonons) is presented. In the static regime, when the inductance is threaded by an external fixed magnetic flux, the usual periodic behavior in the persistent electrical current (frequency q e /ℏ) becomes altered. A new harmonic appears which is twice that of the fundamental (2q e /ℏ). All this is the consequence of the geometric static deformation in the inductance produced by the persistent electrical current itself (Lorentz force).