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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Improved error estimates of the splitting methods for the long-time dynamics for the weakly nonlinear Schrodinger equations
弱非线性薛定谔方程 长时间动力学 分裂方法 误差估计
2023/4/21
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonrelativistic limit of the Klein-Gordon equations: convergence rates and long time approximations
克莱因-戈登方程 非相对论极限 收敛率 长时间近似
2023/4/18
We study the nonrelativistic limit of the cubic Klein-Gordon equations. We show the cubic Klein-Gordon equation converges to the cubic Schr\"odinger equation with a convergence rate of order $\epsilon...
Aheart surgeon doesn’t need to grasp quantum mechanics to perform successful operations. Even chemists don’t always need to know these fundamental principles to study chemical reactions. But the worki...
LIGO detects gravitational waves for third time
LIGO detects gravitational waves third time
2017/7/21
The collision of a pair of colossal, stellar-mass black holes has made itself heard, nearly 3 billion light years away, through a cosmic microphone on Earth.
On Jan. 4, the Laser Interferometry Gravi...
Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems
Quantum monte carlo procedures discretization discrete Hilbert space green's function
2014/12/22
We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated directly in continuous time, rendering the scheme exact. For an ar...
An Adaptive Finite Element Method for the H-Ψ Formulation of Time-Dependent Eddy Current Problems
Maxwell’s equations eddy current problem adaptive finite element method multiply
2012/8/7
In this paper, we develop an adaptive finite element method based on reliable
and efficient a posteriori error estimates for the H − formulation of eddy current problems with
multiply connec...
A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation
A Family of Exact Analytic Time Dependent Packet Solutions Nonlinear Schroedinger Equation Mathematical Physics
2012/6/19
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The N...
A time-splitting spectral scheme for the Maxwell-Dirac system
Maxwell-Dirac system time-splitting spectral method semi-classical asymptotics WKB-expansion
2012/5/24
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic reg...
On the divergence of time-dependent perturbation theory applied to laser-induced molecular transitions: Analytical calculations (1)
time-dependent perturbation theory laser-induced molecular transitions Analytical calculations Mathematical Physics
2012/4/18
Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in we...
Magnetized dark energy and the late time acceleration
Magnetized dark energy the late time acceleration
2012/4/19
In the present work we have searched the existence of the late time acceleration of the Universe. The matter source that is responsible for the late time acceleration of the Universe consists of cosmi...
People used to establish physical laws on the mathematical frame directly, without considering the existence of the No-Shape-Substance. We believe such physical laws are separated from their nature. S...
Embeddings and time evolution of the Schwarzschild wormhole
Einstein-Rosen bridge Schwarzschild wormhole embedding
2011/10/9
Abstract: We show how to embed spacelike slices of the Schwarzschild wormhole (or Einstein-Rosen bridge) in R^3. Graphical images of embeddings are given, including depictions of the dynamics of this ...
Time domain radiation and absorption by subwavelength sources
Time domain radiation absorption subwavelength sources elementary sources
2011/8/5
Abstract: Radiation by elementary sources is a basic problem in wave physics. Although computations of radiated fields in the time domain are textbook examples, the emitted energy flux is usually comp...
Framework for discrete-time quantum walks and a symmetric walk on a binary tree
discrete-time quantum walks symmetric walk Framework Quantum Physics
2011/10/9
Abstract: We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which t...
Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders
Arbitrary-order Hilbert spectral analysis time series wavelet leaders
2011/8/5
Abstract: In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series dir...