[書籍][B] Mathematical concepts of quantum mechanics
SJ Gustafson, IM Sigal, IM Sigal, I Physicien, IM Sigal… - 2003 - Springer
Stephen J. Gustafson Israel Michael Sigal Third Edition Page 1 Universitext Stephen J.
Gustafson Israel Michael Sigal Mathematical Concepts of Quantum Mechanics Third Edition …
Gustafson Israel Michael Sigal Mathematical Concepts of Quantum Mechanics Third Edition …
Derivation of the Cubic NLS and Gross–Pitaevskii Hierarchy from Manybody Dynamics in d = 3 Based on Spacetime Norms
T Chen, N Pavlović - Annales Henri Poincaré, 2014 - Springer
We derive the defocusing cubic Gross–Pitaevskii (GP) hierarchy in dimension d= 3, from an
N-body Schrödinger equation describing a gas of interacting bosons in the GP scaling, in …
N-body Schrödinger equation describing a gas of interacting bosons in the GP scaling, in …
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 …
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 rigorous derivation of the 3D cubic nonlinear Schrödinger equation with a quadratic trap
X Chen - Archive for Rational Mechanics and Analysis, 2013 - Springer
We consider the dynamics of the three-dimensional N-body Schrödinger equation in the
presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V (N β x) …
presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V (N β x) …
[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 …
[HTML][HTML] On the uniqueness of solutions to the periodic 3D Gross–Pitaevskii hierarchy
In this paper, we present a uniqueness result for solutions to the Gross–Pitaevskii hierarchy
on the three-dimensional torus, under the assumption of an a priori spacetime bound. We …
on the three-dimensional torus, under the assumption of an a priori spacetime bound. We …
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 …
On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics
We consider the 3D quantum many-body dynamics describing a dilute Bose gas with strong
confinement in one direction. We study the corresponding Bogoliubov-Born-Green-Kirkwood …
confinement in one direction. We study the corresponding Bogoliubov-Born-Green-Kirkwood …