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Seminar
FIELD Math:Analysis
DATE February 14 (Fri), 2020
TIME 16:00-17:00
PLACE 8309
SPEAKER Seok, Jinmyoung
HOST Jeong, In-Jee
INSTITUTE 경기대학교
TITLE Quantum classical correspondence between Energy-Casimir minimizers of the gravitational Hartree and Vlasov-Poisson equations
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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