Quantum Level Instability of Transverse Excitation in Electron Flow

In current research we use the effective Schrödinger-Poisson model to study a new kind of quantum level instability in an infinite-wall slab electron system. We use the Madelung fluid representation along with the conventional eigenvalue problem techniques in order to solve the linearized coupled differential equations representing the transverse collective linear excitations in the electron gas of arbitrary degree of degeneracy having a constant perpendicular momentum. It is shown that the energy levels of collective electrostatic excitations are doubly quantized due to coupled interactions between single-electron analogous to the classic problem of a particle in a box and collective Langmuir oscillations, which are modulated over single particle quantum state. We also report a new transverse electron slab current plasmon energy level instability caused by the interplay between the wave-like many-electron dispersion and the destabilizing perpendicular electron drift momentum. We further study in detail the parametric dependence of such instability versus different aspects of the quantum system. Such a quantum-level instability may have important applications in characteristic behavior the plasmonic devices and their frequency response. Parametric quantization of drifting electron fluid in a box may also have broad applications in nanoscale quantum device calibration and measurements.