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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Metric geometric aspects of Einstein manifolds
Einstein流形 度量几何 爱因斯坦流形 黎曼几何
2023/11/29
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global stability of the Minkowski spacetime for the Einstein-Vlasov system
爱因斯坦-弗拉索夫系统 闵可夫斯基时空 全球稳定性
2023/4/21
In this talk, we discuss the global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindbla...
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].
BOSE-EINSTEIN CONDENSATION AT FINITE TEMPERATURES:MEAN FIELD LAWS WITH PERIODIC MICROSTRUCTURE
quantum dynamics Bose-Einstein condensation periodic homogenization finite temperatures two-scale expansion mean field limit
2015/10/16
At finite temperatures below the phase transition point, the Bose-Einstein condensation, the macroscopic occupation of a single quantum state by particles of integer spin, is not complete. In the lang...
The Einstein universe is the conformal compactification of Minkowski space.
It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is
to develop the syntheti...
ANALYSIS OF A BOSE-EINSTEIN MARKOV CHAIN
Convergence rate markov chain stationarity k arcsine
2015/7/8
This paper gives sharp rates of convergence to stationarity for a Markov chain generating Bose-Einstein configurations of n balls in k boxes. The analysis leads to curious identities for the arc...
FLUCTUATIONS OF THE BOSE-EINSTEIN CONDENSATE。
ON THE RENORMALIZED VOLUMES FOR CONFORMALLY COMPACT EINSTEIN MANIFOLDS
THE RENORMALIZED VOLUMES CONFORMALLY COMPACT EINSTEIN MANIFOLDS
2014/4/3
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
ON THE RENORMALIZED VOLUMES FOR CONFORMALLY COMPACT EINSTEIN MANIFOLDS
ON THE RENORMALIZED VOLUMES CONFORMALLY COMPACT EINSTEIN MANIFOLDS
2014/4/3
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
Einstein metrics in projective geometry
projective differential geometry Einstein metrics conformal differential geometry
2012/7/11
It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined...
On the classification of homogeneous Einstein metrics on generalized flag manifolds with $b_2(M)=1$
Homogeneous Einstein metric flag manifold second Betti number finiteness conjecture twistor fibration
2012/6/25
We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G/H$ with second Betti number $b_{2}(G/H)=1$. There are 33 such manifolds which have...
Einstein metrics and Yamabe invariants of weighted projective spaces
Einstein metrics Yamabe invariants weighted projective spaces Differential Geometry
2012/6/25
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe in...
张志涛研究员等在Bose-Einstein Condensates和Volterra-Lotka竞争系统研究中取得重要成果
张志涛研究员 Bose-Einstein Condensates Volterra-Lotka 竞争系统 研究 成果 极限
2012/2/23
自从物理学家提出用耦合Gross-Pitaevskii方程组来描述Bose-Einstein凝聚态以来，对这个奇异扰动的Schrodinger方程组及其极限中的phase separation现象出现了大量的研究, 许多国际著名数学家如现代变分理论创始人A. Ambrosetti以及E.N.Dancer,S.Terracini, T. Bartsch,Juncheng Wei等都有突出成果。
Bose-Einstein condensates in optical lattices: mathematical analysis and analytical approximate formulae
Bose-Einstein condensates stability of ground states analytical approximate formulae repulsive or attractive interatomic interactions
2011/9/6
Abstract: We show that the Gross-Pitaevskii equation with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, ...