A linear, finite-dimensional quantum version of the Vlasov-Poisson system is built by second quantization, and small simulations show it reproduces nonlinear plasma oscillations.
Application de la théorie des équations intégrales linéaires aux systèmes d’équations différentielles non linéaires.Acta Math, 59:63, 1932
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Second quantization of nonlinear Vlasov-Poisson system for quantum computation
A linear, finite-dimensional quantum version of the Vlasov-Poisson system is built by second quantization, and small simulations show it reproduces nonlinear plasma oscillations.