Phase-space evolution of quasiparticle excitations in electron gas

Abstract

In this research, we use the dual lengthscale quasiparticle model for collective quantum excitations in electron gas to study the time evolution of the Wigner function. The linearized time-dependent Schrödinger–Poisson system for quasiparticles is used to study the dynamics of initial known stationary and damped solutions in an electron gas with arbitrary degree of degeneracy. The self-consistent potential in the Schrödinger–Poisson model is treated in a quite different manner in this analysis due to the effective coupling of the electrostatic field to the electron density, which leads to a modified Wigner function. It is shown that the modified Wigner function in the absence of external potential evolves similar to the system of free particles, a feature of collective quantum excitations which is quite analogous to freely evolving classical system of particles in the center of mass frame in the absence of external forces. The time evolution of the modified Wigner function reveals a grinding effect on large-amplitude density structures present at initial states, which is a characteristic feature of the Landau damping in plasmas. It is further shown that linear phase-space dynamics of spill-out electrons (damped quasiparticles) can be described similar to free quasiparticles with imaginary momentum. The later predicts the surface electron tunneling via the collective excitations of spill-out electrons at the half-space boundary, which is closely related to the Heisenberg's uncertainty principle. Current research can have applications in plasmonics and related fields.