Mean field dynamics of a quantum tracer particle interacting with a boson gas |
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Authors: | Thomas Chen Avy Soffer |
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Affiliation: | 1. Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA;2. Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA;3. Department of Mathematics and Applied Mathematics, Central China Normal University, Wuhan, China |
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Abstract: | We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in . The pair interactions of the bosons are of mean-field type, with coupling strength proportional to where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit . Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. |
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Keywords: | Bose gas Mean field limit Tracer particle Well-posedness |
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