Chen, Thomas; Soffer, Avy Mean field dynamics of a quantum tracer particle interacting with a boson gas. (English) Zbl 1414.82026 J. Funct. Anal. 276, No. 3, 971-1006 (2019). The paper considers the interaction of a heavy probe particle embedded in a three-dimensional bosonic gas of \(N\) particles. It is assumed that the strength of the boson-boson interaction in the gas scales as \(1/N\) while the mass of the tracer scales as \(N\). A mean-field (Hartree-type) equation for the tracer’s wave function is derived, which looks like a Gross-Pitaevskii equation with nonlocal cubic nonlinearity. Well-posedness of that equation is rigorously proved. Reviewer: Boris A. Malomed (Tel Aviv) Cited in 4 Documents MSC: 82C40 Kinetic theory of gases in time-dependent statistical mechanics 81V70 Many-body theory; quantum Hall effect 35Q40 PDEs in connection with quantum mechanics 82D05 Statistical mechanics of gases Keywords:mean-field approximation; Hartree equation; Gross-Pitaevskii equation; well-posedness PDFBibTeX XMLCite \textit{T. Chen} and \textit{A. Soffer}, J. Funct. Anal. 276, No. 3, 971--1006 (2019; Zbl 1414.82026) Full Text: DOI arXiv References: [1] Bach, V.; Breteaux, S.; Chen, T.; Fröhlich, J.; Sigal, I. M., The time-dependent Hartree-Fock-Bogoliubov equations for bosons [2] Bach, V.; Chen, T.; Faupin, J.; Fröhlich, J.; Sigal, I. M., Effective dynamics of an electron coupled to an external potential in non-relativistic QED, Ann. Henri Poincaré, 14, 6, 1573-1597, (2013) · Zbl 1275.81091 [3] Bach, V.; Chen, T.; Fröhlich, J.; Sigal, I. M., The renormalized electron mass in non-relativistic QED, J. Funct. 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