Thursday, April 3, 2025 - 11:00
Aula dottorato,
Dipartimento di Matematica,
Università degli Studi di Milano,
Via Cesare Saldini 50.
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SPEAKER: Antoine Borie (Université de Rennes)
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Scattering for the positive density Hartree equation
In this talk, we explore the long-time behavior of solutions to of the positive density Hartree equation, which models the evolution of a homogeneous quantum gas. Our focus is the stability of certain stationary states, extending the original result introduced by Mathieu Lewin and Julien Sabin to higher dimensions and more singular interaction potentials. Using tools from dispersive partial differential equations, such as Strichartz estimates and fractional Leibniz rules, we develop a new approach tailored to density matrices.
This talk is based on joint work with Julien Sabin (Rennes University ) and Sonae Hadama (Kyoto University).
