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Nonlinear longitudinal current generated by N transversal electromagnetic waves in the quantum plasma

Quantum plasma with arbitrary degree of degeneration of electronic gas is considered. In plasma N (N>2) external electromagnetic waves are propagated. It is required to find the response of plasma to these waves. From kinetic Wigner equation for quantum collisionless plasmas distribution function in square-law approach on quantities of vector potentials of N electric fields is received. The formula for electric current calculation is deduced at arbitrary temperature, i.e. at arbitrary degree of degeneration of electronic gas. It is shown, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This longitudinal current is orthogonal to the known transversal current received at the linear analysis. The case of small values of wave number is considered. It is shown, that in case of small values of wave numbers the longitudinal current in quantum plasma coincides with a longitudinal current in classical plasma.