Dynamics of ion-acoustic waves in multi-species quantum plasmas with arbitrary degeneracy

The basic properties of ion-acoustic waves are studied in a nonrelativistic, unmagnetized quantum plasma consisting of positive and negative ions and Fermi-Dirac distributed electrons of arbitrary degeneracy. The formation of arbitrary amplitude oscillatory wave structures is investigated both analytically and numerically by employing pseudopotential formalism. The dispersion relation is derived to discuss the linear properties, whereas the nonlinear features of the ion-acoustic wave structures are scrutinized by formulating the dynamical system, then the concept of phase plane analysis, Poincare' map, and Lyapunov exponents are used to explore the system. The essential nonlinear characteristics of quantum ion-acoustic waves are found to have significant qualitative variation depending on the parameters like quantum diffraction(H), phase speed(M), etc. In the fully nonlinear regime, the considered plasma system exhibits some very important nonlinear structures like chaotic and hyper-chaotic trajectories. Irregular periodic oscillation is found to be present in subsonic(M<1) region, whereas the ion-acoustic wave shows aperiodic nature in the supersonic(M > 1) region. In order to prove the existence of chaotic and hyper-chaotic trajectories, the notion of Lyapunov exponent is employed. The obtained results of this investigation cover the basic quantum effects in plasmas for both the high and low-temperature regimes which are reasonably fruitful for studying laser-produced plasmas in the laboratory as well as some high-density astrophysical plasma situations such as white dwarfs and neutron stars.