Nonlinear waves and coherent structures in the quantum single-wave model

Abstract

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the quantum single-wave model has been studied, and periodic in time patterns have been found both analytically and numerically. In addition, some features of quantum chaos have been detected in the unstable region in parameter space. Further, a class of standing-wave solutions of the quantum singlewave model has also been found, which have been observed to behave as stable solitary-wave structures. The analytical results have been finally compared to the exact system dynamics obtained by solving the corresponding equations in Schrodinger representation numerically.

Nonlinear low-frequency collisional quantum Buneman instability

“…Also, in the near future the development of coherent brilliant X-ray radiation sources [11] and keV free electron lasers [12] will provide experimental access to the quantum nature of plasmas under extreme conditions. Some of the most recent developments in the field are the analysis of wave breaking in quantum plasmas [13], the characteristics of bounded quantum plasmas including electron exchange-correlation effects [14], the development of a quantum single-wave theory for nonlinear coherent structures in quantum plasmas [15], the discussion of waves in quantum dusty plasmas [16], the prediction of a fundamental size limit for plasmonic devices due to the quantum broadening of the transition layer [17], as well as the inclusion of spin [18] and relativistic [19] effects in quantum plasma modeling. Finally, we note the usefulness of quantum plasma techniques to other, closely related problems, such as the treatment of nonlinear wave propagation in gravitating Bose-Einstein condensates [20].…”