Bogoliubov corrections and trace norm convergence for the Hartree dynamics
D Mitrouskas, S Petrat, P Pickl - Reviews in Mathematical Physics, 2019 - World Scientific
We consider the dynamics of a large number N of nonrelativistic bosons in the mean field
limit for a class of interaction potentials that includes Coulomb interaction. In order to …
limit for a class of interaction potentials that includes Coulomb interaction. In order to …
[BOOK][B] Effective evolution equations from quantum dynamics
In these notes we review the material presented at the summer school on “Mathematical
Physics, Analysis and Stochastics” held at the University of Heidelberg in July 2014. We …
Physics, Analysis and Stochastics” held at the University of Heidelberg in July 2014. We …
Gross–Pitaevskii dynamics for Bose–Einstein condensates
We study the time-evolution of initially trapped Bose–Einstein condensates in the Gross–
Pitaevskii regime. We show that condensation is preserved by the many-body evolution and …
Pitaevskii regime. We show that condensation is preserved by the many-body evolution and …
Quantitative Derivation of the Gross‐Pitaevskii Equation
Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of
Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross …
Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross …
Bose–Einstein condensation with optimal rate for trapped bosons in the Gross–Pitaevskii regime
We consider a Bose gas consisting of N particles in R 3, trapped by an external field and
interacting through a two-body potential with scattering length of order N-1. We prove that …
interacting through a two-body potential with scattering length of order N-1. We prove that …
Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger
N Rougerie - EMS Surveys in Mathematical Sciences, 2021 - ems.press
How and why could an interacting system of many particles be described as if all particles
were independent and identically distributed? This question is at least as old as statistical …
were independent and identically distributed? This question is at least as old as statistical …
Asymptotic expansion of low-energy excitations for weakly interacting bosons
We consider a system of N bosons in the mean-field scaling regime for a class of
interactions including the repulsive Coulomb potential. We derive an asymptotic expansion …
interactions including the repulsive Coulomb potential. We derive an asymptotic expansion …
Optimal rate of condensation for trapped bosons in the Gross–Pitaevskii regime
Abstract We study the Bose–Einstein condensates of trapped Bose gases in the Gross–
Pitaevskii regime. We show that the ground state energy and ground states of the many …
Pitaevskii regime. We show that the ground state energy and ground states of the many …
[HTML][HTML] On time dependent Schrödinger equations: Global well-posedness and growth of Sobolev norms
In this paper we consider time dependent Schrödinger linear PDEs of the form i∂ t ψ= L (t)
ψ, where L (t) is a continuous family of self-adjoint operators. We give conditions for well …
ψ, where L (t) is a continuous family of self-adjoint operators. We give conditions for well …
Quantum fluctuations of many-body dynamics around the Gross–Pitaevskii equation
We consider the evolution of a gas of N bosons in the three-dimensional Gross–Pitaevskii
regime (in which particles are initially trapped in a volume of order one and interact through …
regime (in which particles are initially trapped in a volume of order one and interact through …