Quantum corrected liouville model: Mathematical analysis

A quantum corrected dynamical model for charged particles is derived. The corrections to the Newton motion are obtained within the Liouville formalism and are expressed by an effective nonlinear force. This effective force describes the non-local character of the quantum particles. The well posedness of the quantumcorrected problem is studied from the mathematical point of view. Existence and uniqueness of the solution are proved for a mollified version of the effective force. Numerical tests are performed and the range of validity of the model is investigated.