Simple Wigner-Langevin equation


A new dynamical equation is derived by substituting the Schrödinger-LangevinKostin equation into the definition for the Wigner function, it can be called the quantumclassical Wigner-Langevin equation. The proposed equation contains partial derivatives for time and phase space variables of the Wigner function, its coefficients are spatial derivatives of potentials that take into account friction, white noise and external influence. The transition to the classical regime of motion is also discussed.