Matter waves, single-mode excitations of the matter-wave field, and the atomtronic transistor oscillator

A self-consistent theoretical treatment of a triple-well atomtronic transistor circuit reveals the mechanism gain, conditions oscillation, and properties subsequent coherent matter waves emitted by circuit. Bose-condensed reservoir atoms in large source well provides chemical potential that drives dynamics. The theory is based on ansatz condensate arises gate as displaced ground state, is, one undergoes dipole oscillation well. That remain condensed oscillating shown to be consequence cooling induced emission wave into vacuum. Key parameters such transconductance output current are derived transitioning classical equivalent model. Voltage-like current-like matter-wave fields introduced analogy with microwave circuits, an impedance relationship between two. This leads notion classically dual electromagnetic which distinct from de Broglie associated cold atoms. Subjecting atom flux atomic will reduce wavelength, for example, increase wavelength. Quantization photon identified not but something else, here dubbed ``matteron.''