W. A. Salem, T. Chen, and V. Vougalter, On the well-posedness of the semi-relativistic Schr??dinger-Poisson system, Dynamics of Partial Differential Equations, vol.9, issue.2, pp.121-132, 2012.
DOI : 10.4310/DPDE.2012.v9.n2.a2

W. A. Salem, T. Chen, and V. Vougalter, On the generalized semi-relativistic Schrödinger-Poisson system in R n, Doc. Math, vol.18, pp.343-357, 2013.

W. A. Salem, T. Chen, and V. Vougalter, Existence and nonlinear stability of stationary states for the semi-relativistic Schrödinger-Poisson system, pp.1171-1196, 2014.

I. Anapolitanos, Rate of Convergence Towards the Hartree???von Neumann Limit in the Mean-Field Regime, Letters in Mathematical Physics, vol.52, issue.3, pp.1-31, 2011.
DOI : 10.1103/RevModPhys.52.569

I. Anapolitanos and I. M. Sigal, The Hartree-von Neumann limit of many body dynamics

J. Barbaroux and V. Vougalter, Existence and nonlinear stability of stationary states for the magnetic Schrödinger- Poisson system, J. Math. Sci, vol.219, pp.6-874, 2016.
DOI : 10.1007/s10958-016-3152-z

F. Brezzi and P. Markowich, The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation, Mathematical Methods in the Applied Sciences, vol.40, issue.1, pp.35-61, 1991.
DOI : 10.1007/978-1-4612-5561-1

K. Broderix, H. Leschke, and P. Müller, Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections, J. Funct. Anal, vol.15, issue.212, pp.287-323, 2004.
DOI : 10.1016/j.jfa.2004.01.009
URL : https://doi.org/10.1016/j.jfa.2004.01.009

T. Cazenave and M. J. Esteban, On the stability of stationary states for nonlinear Schrödinger equations with an external magnetic field, Mat. Apl. Comput, vol.7, issue.3, pp.155-168, 1988.

A. D. Bouard, Nonlinear Schröedinger equations with magnetic fields, Differential Integral Equations, vol.4, issue.1, pp.73-88, 1991.

R. Illner, P. F. Zweifel, and H. Lange, Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schr??dinger-Poisson systems, Mathematical Methods in the Applied Sciences, vol.40, issue.5, pp.349-376, 1994.
DOI : 10.1007/978-1-4612-6027-1

P. Lax, Integrals of nonlinear equations of evolution and solitary waves, Communications on Pure and Applied Mathematics, vol.15, issue.5, pp.467-490, 1968.
DOI : 10.1080/14786449508620739

P. A. Markowich, G. Rein, and G. Wolansky, Existence and nonlinear stability of stationary states of the Schrödinger- Poisson system, J. Stat. Phys, vol.106, pp.5-6, 2002.

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1983.
DOI : 10.1007/978-1-4612-5561-1

M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis and Self-Adjointness, 1975.

H. Spohn, Kinetic equations from Hamiltonian dynamics: Markovian limits, Reviews of Modern Physics, vol.7, issue.3, pp.569-615, 1980.
DOI : 10.1016/0021-9991(71)90109-4

H. Steinrück, The One-Dimensional Wigner???Poisson Problem and Its Relation to the Schr??dinger???Poisson Problem, SIAM Journal on Mathematical Analysis, vol.22, issue.4, pp.957-972, 1991.
DOI : 10.1137/0522061