| Abstract: |
| For the gravitational Vlasov-Poisson equation, Guo and Rein constructed a class of classical isotropic states as minimizers of free energies (or energy-Casimir functionals) under the mass constraints. For the quantum counterpart, that is, the gravitational Hartree equations, isotropic states as free energy minimizers are constructed by Aki, Dolbeault and Sparber. In this talk, we are concerned with the correspondence between quantum and classical isotropic states. Precisely, we prove that as the Planck constant goes to zero, free energy minimizers for the Hartree equation converge to those for the Vlasov equation in terms of potential functions as well as via the Wigner transform/Toplitz quantization. |
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