On the Emergence of Quantum Boltzmann Fluctuation Dynamics near a Bose–Einstein Condensate

We study the mean-field and semiclassical limit of the quantum many-body dynamics with a repulsive δ-type potential N 3β V (N β x) and a Coulomb potential, which leads to a macroscopic fluid equation, the Euler-Poisson equation with pressure. We prove quantitative strong convergence of the quantum mass and momentum densities up to the first blow up time of the limiting equation. The main ingredient is a functional inequality on the δ-type potential for the almost optimal case β ∈ (0, 1), for which we give an analysis of the singular correlation structure between particles.

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An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff

Yang,

Zhou

2024

Journal of Functional Analysis

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On the Emergence of Quantum Boltzmann Fluctuation Dynamics near a Bose–Einstein Condensate

Cited by 3 publications

References 252 publications

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From Incommensurate Bilayer Heterostructures to Allen–Cahn: An Exact Thermodynamic Limit

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An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff

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