Investigation of the modified Vlasov equation

Perepelkin E.E., Sadovnikov B.I., Inozemtseva N.G., Suchkov D.A.

Moscow State University, Faculty of Physics, Department of Quantum Statistics and Field Theory

This paper revises traditional phenomenological approaches to the application of Vlasov equation to describe the dissipative systems. The classical Vlasov equation, that widely used in scientific literature, differs from the original Vlasov equation, that was obtained by A.A. Vlasov himself. The original Vlasov equation contains non-zero right-hand side, as a result, as it shown in this paper, can be used to describe dissipative systems, unlike the classical Vlasov equation.

In this paper n-body system in harmonic oscillator considered. Systems with and without dissipative forces considered. The exact solution for all systems obtained via the modified Vlasov equation, that follows from the original Vlasov equation naturally. Also, numerical computation performed. A good agreement of numerical results with theoretical predictions in all cases is observed. Due to the complexity of the calculations, massively parallel computations were used on graphics accelerators using CUDA technology.

In conclusion, the results of this work are discussed.

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