The derivation of the Boltzmann equation from quantum many-body dynamics
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive
rigorously the quantum Boltzmann equation, which contains the classical hard sphere model …
rigorously the quantum Boltzmann equation, which contains the classical hard sphere model …
Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation
We consider the dynamics of N bosons in 1D. We assume that the pair interaction is
attractive and given by N^ β-1 V (N^ β.) where N β-1 V (N β). where ∫ V\leqslant 0∫ V⩽ 0 …
attractive and given by N^ β-1 V (N^ β.) where N β-1 V (N β). where ∫ V\leqslant 0∫ V⩽ 0 …
Well-posedness of the nonlinear Schrödinger equation on the half-plane
AA Himonas, D Mantzavinos - Nonlinearity, 2020 - iopscience.iop.org
The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (NLS) equation on
the half-plane with nonzero boundary data is studied by advancing a novel approach …
the half-plane with nonzero boundary data is studied by advancing a novel approach …
Correlation structures, many-body scattering processes, and the derivation of the Gross–Pitaevskii hierarchy
We consider the dynamics of bosons in three dimensions. We assume that the pair
interaction is given by. By studying an associated many-body wave operator, we introduce a …
interaction is given by. By studying an associated many-body wave operator, we introduce a …
The derivation of the energy-critical NLS from quantum many-body dynamics
We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-
body interaction in the T^ 3 T 3 (periodic) setting. Due to the known complexity of the energy …
body interaction in the T^ 3 T 3 (periodic) setting. Due to the known complexity of the energy …
On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
We consider the 3D quantum BBGKY hierarchy which corresponds to the N-particle
Schrödinger equation. We assume the pair interaction is N3β− 1V (Nβ·). For the interaction …
Schrödinger equation. We assume the pair interaction is N3β− 1V (Nβ·). For the interaction …
[HTML][HTML] A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on T3 from the dynamics of many-body quantum systems
V Sohinger - Annales de l'Institut Henri Poincaré C, Analyse non …, 2015 - Elsevier
In this paper, we will obtain a rigorous derivation of the defocusing cubic nonlinear
Schrödinger equation on the three-dimensional torus T 3 from the many-body limit of …
Schrödinger equation on the three-dimensional torus T 3 from the many-body limit of …
The rigorous derivation of the 2D cubic focusing NLS from quantum many-body evolution
We consider a 2D time-dependent quantum system of-bosons with harmonic external
confining and attractive interparticle interaction in the Gross–Pitaevskii scaling. We derive …
confining and attractive interparticle interaction in the Gross–Pitaevskii scaling. We derive …
Derivation of the time dependent Gross–Pitaevskii equation in two dimensions
M Jeblick, N Leopold, P Pickl - Communications in Mathematical Physics, 2019 - Springer
We present microscopic derivations of the defocusing two-dimensional cubic nonlinear
Schrödinger equation and the Gross–Pitaevskii equation starting from an interacting N …
Schrödinger equation and the Gross–Pitaevskii equation starting from an interacting N …
Focusing quantum many-body dynamics, II: The rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation from 3D
We consider the focusing 3D quantum many-body dynamic which models a dilute Bose gas
strongly confined in two spatial directions. We assume that the microscopic pair interaction is …
strongly confined in two spatial directions. We assume that the microscopic pair interaction is …