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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/5/12
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
It is a great pleasure to announce the 7th Workshop on Quantum Many-Body Computation, which will be held in Beijing from May 5 to 7, 2017. This workshop is organized by the University of Chinese Acade...
A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM
Dispersive estimates interaction Morawetz type (correlation) estimates many-body Hamiltonian many-body Schrodinger equation quantum hydrodynamics BBGKY hierarchy
2015/10/16
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
BOSE–EINSTEIN CONDENSATION BEYOND MEAN FIELD:MANY-BODY BOUND STATE OF PERIODIC MICROSTRUCTURE
Bose–Einstein condensation homogenization many-body perturbation theory two-scale expansion singular perturbation mean field limit bound state
2015/10/16
We study stationary quantum fluctuations around a mean field limit in trapped, dilute atomic gases of repulsively interacting bosons at zero temperature. Our goal is to describe quantum-mechanically t...
ERRATUM:BOSE–EINSTEIN CONDENSATION BEYOND MEAN FIELD:MANY-BODY BOUND STATE OF PERIODIC MICROSTRUCTURE
Bose–Einstein condensation homogenization many-body perturbation theory two-scale expansion singular perturbation mean field limit bound state
2015/10/16
This is a correction to the author’s article [Multiscale Model. Simul.,10 (2012), pp.383–417].
NON-COLLISION SINGULARITIES IN THE PLANAR TWO-CENTER-TWO-BODY PROBLEM
PLANAR TWO-CENTER-TWO-BODY PROBLEM NON-COLLISION SINGULARITIES
2015/9/29
Statement of the main result. We study a two-center two-body problem.
Consider two xed centers Q1 and Q2 of masses m1 = m2 = 1 located at distance
from each other and two small particles Q3 and Q4...
Global instability in the elliptic restricted three body problem
Elliptic Restricted Three Body problem Arnold diffusion splitting of separatrices Melnikov integral
2015/9/25
The (planar) ERTBP describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of m...
DESTRUCTION OF INVARIANT CURVES IN THE RESTRICTED CIRCULAR PLANAR THREE-BODY PROBLEM BY USING COMPARISON OF ACTION
INVARIANT CURVES RESTRICTED CIRCULAR PLANAR THREE-BODY PROBLEM
2015/9/25
The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle al...
THE METHOD OF SPREADING CUMULATIVE TWIST AND ITS APPLICATION TO THE RESTRICTED CIRCULAR PLANAR THREE BODY PROBLEM
SPREADING CUMULATIVE TWIST RESTRICTED CIRCULAR PLANAR THREE BODY PROBLEM
2015/9/25
The purpose of this paper is twofold. First we show that the dynamics ofa Sun-Jupiter-Comet system and under some simplifying assumptions has a semi-infiniteregion of instability. This is done by redu...
On Hausdorff dimension of oscillatory motions in three body problems
Hausdorff dimension oscillatory motions three body problems
2015/9/25
We show that for the Sitnikov example and for the restricted planar circular 3–body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains fo...
A continuum of periodic solutions to the planar four-body problem with various choices of masses
periodic solutions planar four-body problem various choices of masses
2015/3/18
A continuum of periodic solutions to the planar four-body problem with various choices of masses.
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem
Sturm-Liouville eigenvalue applications n-body problem
2015/3/18
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem.
Lambert’s theorem, convex optimization, and minimizing solutions of the n-body problems
Lambert’s theorem convex optimization minimizing solutions n-body problems
2015/3/18
Lambert’s theorem, convex optimization, and minimizing solutions of the n-body problems.
Escape, collisions and regularization in the variational approach to the N-body problem
Escape collisions regularization variational approach N-body problem
2015/3/18
Escape, collisions and regularization in the variational approach to the N-body problem.
The planar circular restricted three body problem in the lunar case
The planar circular restricted three body problem lunar case
2015/3/18
The course is a short introduction to some aspects of the simplest non-integrable three body problem, the study of which goes back to the seminal works of Hill, Poincar′e and Birkhoff. After Goursat (...