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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Random phase approximation for the mean-field electron gas （3）
平均场 电子气 随机相位近似
2023/11/29
Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons.I.
Second-Order Corrections Mean Field Evolution Weakly Interacting Bosons
2015/10/16
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
Second-order corrections to mean field evolution of weakly interacting Bosons.II
Second-order corrections Mean field evolution Weakly interacting bosons
2015/10/16
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
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...
SECOND ORDER CORRECTIONS TO MEAN FIELD EVOLUTION FOR WEAKLY INTERACTING BOSONS, I
SECOND ORDER equation
2015/10/15
Inspired by the works of Rodnianski and Schlein [31]
and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation
that describes a second-order correction to the usual tensor product (mean-ʂ...
SECOND-ORDER CORRECTIONS TO MEAN FIELD EVOLUTION OF WEAKLY INTERACTING BOSONS. II
SECOND-ORDER WEAKLY INTERACTING BOSONS
2015/10/15
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a second-order correction
to a mean-field e...
PAIR EXCITATIONS AND THE MEAN FIELD APPROXIMATION OF INTERACTING BOSONS, I
PAIR EXCITATIONS MEAN FIELD APPROXIMATION
2015/10/15
In our previous work [20],[21] we introduced a correction to the mean eld approximation of interacting Bosons. This
correction describes the evolution of pairs of particles that leave
the condensat...
BEYOND MEAN FIELD: ON THE ROLE OF PAIR EXCITATIONS IN THE EVOLUTION OF CONDENSATES
BEYOND MEAN FIELD PAIR EXCITATIONS
2015/10/15
This paper is in part a summary of our earlier work
[17, 18, 19], and in part an announcement introducing a re nement
of the equations for the pair excitation function used in our previous work with...
Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo
Diagram to monte carlo illustration skeleton diagram lattice model the propagators single particle
2014/12/19
The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feyn- man's diagrammatic series using skeleton diagrams. For lattice models the eciency of BDMC can be dramatically im...
Extremal Functions for a Mean Field Equation in Two Dimension
Extremal Functions a Mean Field Equation Two Dimension
2014/4/3
Let be a bounded piecewise C 2 simply-connected domain. In thisarticle, we give necessary and sucient conditions for the existence ofmaximizer ofJ8( ) = log Zedx!116Zj 5 j2dx for 2 H10(). We pro...
Asymptotics of the mean-field Heisenberg model
Asymptotics the mean-field Heisenberg model Mathematical Physics
2012/4/16
We consider the mean-field classical Heisenberg model and obtain detailed information about the magnetization by studying the model on a complete graph and sending the number of vertices to infinity. ...
Asymptotics of the Invariant Measure in Mean Field Models with Jumps
decoupling approximation fluid limit invariant measure McKean-Vlasov equation mean field limit small noise limit
2011/9/16
Abstract: We consider the asymptotics of the invariant measure for the process of the spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects th...
Study of the neutron skin thickness of ${}^{208}$Pb in mean field models
mean field models
2011/7/20
We study whether the neutron skin thickness $\Delta r_{np}$ of ${}^{208}$Pb originates from the bulk or from the surface of the neutron and proton density distributions in mean field models.