[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 …
[書籍][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 …
Low regularity exponential-type integrators for semilinear Schrödinger equations
A Ostermann, K Schratz - Foundations of Computational Mathematics, 2018 - Springer
We introduce low regularity exponential-type integrators for nonlinear Schrödinger
equations for which first-order convergence only requires the boundedness of one …
equations for which first-order convergence only requires the boundedness of one …
Negative Energy Ground States for the L 2-Critical NLSE on Metric Graphs
We investigate the existence of ground states with prescribed mass for the focusing
nonlinear Schrödinger equation with L 2-critical power nonlinearity on noncompact quantum …
nonlinear Schrödinger equation with L 2-critical power nonlinearity on noncompact quantum …
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 …
Quantum many-body fluctuations around nonlinear Schrödinger dynamics
We consider the many-body quantum dynamics of systems of bosons interacting through a
two-body potential N^ 3 β-1 V (N^ β x) N 3 β-1 V (N β x), scaling with the number of particles …
two-body potential N^ 3 β-1 V (N^ β x) N 3 β-1 V (N β x), scaling with the number of particles …
[書籍][B] An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog
T Tao - 2022 - books.google.com
In 2007 Terry Tao began a mathematical blog to cover a variety of topics, ranging from his
own research and other recent developments in mathematics, to lecture notes for his …
own research and other recent developments in mathematics, to lecture notes for his …
Mean‐Field Evolution of Fermionic Mixed States
In this paper we study the dynamics of fermionic mixed states in the mean‐field regime. We
consider initial states that are close to quasi‐free states and prove that, under suitable …
consider initial states that are close to quasi‐free states and prove that, under suitable …
Unconditional Uniqueness for the Cubic Gross‐Pitaevskii Hierarchy via Quantum de Finetti
We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic
Gross‐Pitaevskii hierarchy in. One of the main tools in our analysis is the quantum de Finetti …
Gross‐Pitaevskii hierarchy in. One of the main tools in our analysis is the quantum de Finetti …
Second order corrections to mean field evolution for weakly interacting bosons in the case of three-body interactions
X Chen - Archive for Rational Mechanics and Analysis, 2012 - Springer
In this paper, we consider the Hamiltonian evolution of N weakly interacting bosons.
Assuming triple collisions, its mean field approximation is given by a quintic Hartree …
Assuming triple collisions, its mean field approximation is given by a quintic Hartree …