On the time dependence of the rate of convergence towards Hartree dynamics for interacting Bosons

Abstract

We consider interacting $N$-Bosons in three dimensions. It is known that the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$. We investigate the time dependence of the difference. To have sub-exponential bound, we use the results of time decay estimate for small initial data. We also refine time dependent bound for singular potential using Strichartz estimate. We consider the interaction potential $V(x)$ of type $\lambda \exp (-\mu |x|)|x{|}^{-\gamma }$ for $\lambda \in \mathbb{R}$, $\mu \ge 0$, and $0<\gamma <3/2$, which covers the Coulomb and Yukawa interaction.

arXiv commentRemark 1.7 has been refined. Other minor errata ware corrected

References in corpus (10)

• Mean-Field Dynamics: Singular Potentials and Rate of Convergence
• Second-order corrections to mean field evolution for weakly interacting Bosons. I
• Pair excitations and the mean field approximation of interacting Bosons, I
• Rate of Convergence Towards Hartree Dynamics
• Second-order corrections to mean-field evolution of weakly interacting Bosons, II
• Second order corrections to mean field evolution for weakly interacting Bosons in the case of 3-body interactions
• Pair excitations and the mean field approximation of interacting Bosons, II
• Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data
• Rate of Convergence Towards Semi-Relativistic Hartree Dynamics
• Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential

Cited by in corpus (4)

• Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential