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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost periodic function and rotation number of the Schrodinger operator
薛定谔算子 几乎周期函数 旋转数
2023/4/25
The concept of almost periodic functions is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schr?dinger operator is named after E. Schr?dinger. I will present our work relate...
A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials
Schrodinger equation Bloch decomposition time-splitting spectral method semiclassical asymptotics lattice potential
2012/5/24
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics ...
Localization for quasi-periodic Schrodinger operators with dynamics defined by the skew-shift and potential in a Gevrey-class
Mathematical Physics Spectral Theory dynamics quasi-periodic Schrodinger operators
2012/4/16
We consider the discrete one-dimensional Schr\"{o}dinger operator with quasi-periodic potential $v_n := \lambda v (\shift^n \, \xx)$, where $\shift : \T^2 \rightarrow \T^2, \, \shift \xx := (x_1+x_2, ...
Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces
Bloch-Floquet waves thin periodic bi-material strip Mathematical Physics
2011/9/23
Abstract: We analyse an asymptotic low-dimensional model of anti-plane shear in a thin bi-material strip containing a periodic array of interfacial cracks. Both ideal and non-ideal interfaces are cons...
A Model connecting Quantum, Diffusion, Soliton, and Periodic Localized States under Brownian motion
connecting Quantum Diffusion Soliton Brownian motion Mesoscale and Nanoscale Physics
2011/10/9
Abstract: We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but ...
A charged particle in a homogeneous magnetic field accelerated by a time periodic Aharonov-Bohm flux
electron-cyclotron resonance Aharonov-Bohm flux quantum averaging method acceleration rate
2011/9/6
Abstract: We consider a nonrelativistic quantum charged particle moving on a plane under the influence of a uniform magnetic field and driven by a periodically time-dependent Aharonov-Bohm flux. We ob...
Spectral properties of a 2D scalar wave equation with 1D-periodic coefficients
2D scalar wave equation 1D-periodic coefficients
2011/7/26
Spectral properties of a 2D scalar wave equation with 1D-periodic coefficients.
Approximate action-angle variables for the figure-eight and other periodic three-body orbits
the figure-eight other periodic three-body orbits Classical Physics
2011/7/26
Approximate action-angle variables for the figure-eight and other periodic three-body orbits.
Approximate action-angle variables for the figure-eight and other periodic three-body orbits
action-angle variables three-body orbit
2011/9/14
We use the maximally permutation symmetric set of three-body coordinates, that consist of the “hyper-radius” R = p2 + 2, the “rescaled area of the triangle”
p3
2R2 | × |) and the (braiding)
hyp...
Pseudo resonance induced quasi-periodic behavior in stochastic threshold dynamics
Pseudo resonance quasi-periodic behavior stochastic threshold dynamics
2011/7/27
Abstract: Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense th...
Nonequilibrium Fluctuations in a Gaussian Galton Board (or Periodic Lorentz Gas) Using Long Periodic Orbits
Galton Board Lyapunov Spectrum Fluctuations Nonequilibrium
2010/11/19
Predicting nonequilibrium fluctuations requires a knowledge of nonequilibrium distribution functions.Despite the distributions’ fractal character some theoretical results, “Fluctuation Theorems”,remin...
Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
periodic waves solitons the nonlinear Schrodinger equation
2010/11/18
Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a w...
Fitting the Log Periodic Power Law to financial crashes: a critical analysis
Log Periodic Power Law financial crashes critical analysis
2010/4/27
A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain range...
Entangled three-particle states in magnetic field: Periodic correlations and density matrices
quantum entanglement Wigner rotation Lorentz transformation density matrix
2010/3/10
Time evolutions of different types of entangled states of three spin-1/2 particles are studied in the presence of a constant, external magnetic field, which causes the individual spins to precess. Thi...
A periodic orbit formula for quantum reactions through transition states
periodic orbit formula quantum reactions transition states
2010/4/1
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space usin...