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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On constructions of Lax representations: some examples
松弛表示 构造 非线性数学物理方程 KdV方程
2023/4/24
著名数学家Peter Lax 在1968年将重要的非线性数学物理方程---KdV方程表示为一个算子方程， 即给出了KdV方程的Lax表示或Lax对。Lax对在孤立子理论的发展中扮演者重要角色，可以看成是研究可积系统的出发点。但如何构造一个给定非线性系统的Lax表示却是非常困难的问题。本报告在概述Lax表示历史的基础上，以Boris Kupershmidt提出的两个非线性发展型方程为具体例子，介绍L...
三亚国际数学论坛：Black Holes,Quantum Chaos,and Solvable Quantum Systems
三亚国际数学论坛 Black Holes Quantum Chaos Solvable Quantum Systems
2017/11/24
String theory is a consistent mathematical framework for quantum gravity, a deep question in both fundamental physics and mathematics. One of the main achievements during the past two decades is the d...
HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES
HIGGS BUNDLES LOCAL SYSTEMS RIEMANN SURFACES
2015/12/17
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
A steady state capturing and preserving method for computing hyperbolic systems with geometrical source terms having concentrations
Shallow water equations Nozzle flow equations Discontinuous topography well-balanced scheme surface gradient method Shock capturing
2012/8/8
A steady state capturing and preserving method for computing hyperbolic systems with geometrical source terms having concentrations 。
On Collisions in Nonholonomic systems
Nonholonomic mechanics rigid bodies collisions Lagrange-d’Alembert equation
2012/6/27
We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. In the light of this concept we describe dynamics of the collisions. Several ...
Energy fluctuations, hydrodynamics and local correlations in harmonic systems with bulk noises
Energy fluctuations hydrodynamics local correlations harmonic systems Mathematical Physics
2012/6/12
In this note, I summarise and comment on joint work with C. Bernardin, V. Kannan and J. L. Lebowitz concerning two harmonic systems with bulk noises whose nonequilibrium steady states (NESS) are nearl...
A Hamilton-Jacobi Theory for Singular Lagrangian Systems in the Skinner and Rusk Setting
Hamilton-Jacobi theory presymplectic constraint algorithm
2012/5/9
We develop a Hamilton-Jacobi theory for singular lagrangian systems in the Skinner-Rusk formalism. Comparisons with the Hamilton-Jacobi problem in the lagrangian and hamiltonian settings are discussed...
Particle filtering in high-dimensional chaotic systems
particle filtering in high dimensions chaotic systems Lorenz’96 nonlinear filtering dimensional reduction homogenization
2012/4/20
We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posteri...
Third-order superintegrable systems separable in parabolic coordinates
Integrability Superintegrability Separation of Variables Classical and Quantum Mechanics
2012/4/23
In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equations and show that ...
Mathematical Modeling of Finite Quantum Systems
Finite Quantum Systems Quantum Physics High Energy Physics - Theory
2011/10/10
Abstract: We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for th...
On the Supersymmetric Spectra of two Planar Integrable Quantum Systems
Supersymmetric Spectra Planar Integrable Quantum Systems High Energy Physics - Theory
2011/10/9
Abstract: Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both s...
Edge states and topological phases in non-Hermitian systems
Edge states topological phases non-Hermitian systems Mesoscale and Nanoscale Physics
2011/9/30
Abstract: Topological stability of the edge states is investigated for non-Hermitian systems. We examine two classes of non-Hermitian Hamiltonians supporting real bulk eigenenergies in weak non-Hermit...
Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures
Stochastic treatment finite-N effects mean-field systems lifetimes of coherent structures
2011/8/29
Abstract: A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N eff...
Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves
Discrete Integrable Systems Hodograph Transformations Motions of Discrete Plane Curves
2011/9/29
Abstract: We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and t...
Resonances for "large" ergodic systems in one dimension: a review
Resonances random operators periodic operators
2011/8/24
安徽理工大学共建数据
Abstract: The present note reviews recent results on resonances for one-dimensional quantum ergodic systems constrained to a large box. We restrict ourselves to one dimensional models in the discrete ...