Weakly nonlinear interactions of collective oscillations in a correlated degenerate fluid

Abstract

A generalized viscoelastic quantum hydrodynamic model is proposed for the dynamics of strongly correlated degenerate isothermal fluid. The quantum forces associated with the quantum diffraction effect along with the strong correlation effects are embedded in this transport equation through the viscoelastic relaxation of correlations. The collective dynamics of linear and nonlinear modes in such correlated degenerate fluid are also investigated. In the high-frequency oscillation (kinetic regime), the dynamics of the weakly nonlinear mode is found to be governed by a novel equation with a memory dependent non-local nonlinear term that describes the strong correlation effect. This novel equation is solved analytically and numerically. In the low-frequency oscillation (hydrodynamic regime), the weakly nonlinear mode is found to be governed by a Korteweg–de Vries Burgers' equation that exhibits dispersive shock wave. In both the dynamics, quantum diffraction introduces the dispersive effect.