Hydrodynamics of quantum corrections to the Coulomb interaction via the third rank tensor evolution equation: application to Langmuir waves and spin-electron acoustic waves

The quantum effects in plasmas can be described by the hydrodynamics containing continuity and Euler equations. However, novel phenomena are found via extended set of hydrodynamic equations, where pressure evolution equation flux third-rank tensor included. These give corrections to Coulomb interaction. spectra Langmuir waves spin-electron acoustic calculated. application ensures that contribution wave spectrum is proportional $(3/5)v_{\textrm {Fe}}^{2}$ rather than $(1/3)v_{\textrm , $v_{\textrm {Fe}}$ Fermi velocity.