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In 1934, physicist Eugene Wigner made a theoretical prediction based on quantum mechanics that for decades years went unseen.
The quantum scattering limit for a regularized Wigner equation
quantum scattering limit regularized Wigner equation
2015/7/14
We consider a regularized Wigner equation with an oscillatory kernel, the regularization acts in the space variable to damp high frequencies. The oscillatory kernel is directly derived from the Schrod...
Limit of fluctuations of solutions of Wigner Equation
fluctuations of solutions Wigner Equation
2015/7/14
We consider fluctuations of the solution W ε(t, x, k) of the Wigner equation, which describes energy evolution of a solution of the Schr¨odinger equation with a random white noise in time potential. T...
Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential
Fluctuations of solutions Wigner equation Ornstein-Uhlenbeck potential
2015/7/14
We consider energy fluctuations for solutions of the Schrodinger equation with an OrnsteinUhlenbeck random potential when the initial data is spatially localized. The limit of the fluctuations of the ...
Convergence of Semi-discrete Stationary Wigner Equation with Inflow Boundary Conditions
Stationary Wigner equation inflow boundary conditions well-posedness
2014/10/10
Making use of the Whittaker-Shannon interp olation formula w ith shifted sampling p oints, we prop ose in this pap e r a well-p osed semi-discretization of the stationary Wigner equation with inflow B...
A device adaptive in ow boundary condition for Wigner equations of quantum transport
Frensley in ow boundary condition Wigner function Resonant tunneling diode
2014/9/26
In this paper, an improved in
ow boundary condition is proposed for Wigner equa-tions in simulating a resonant tunneling diode (RTD), which takes into consideration
the band structure of the device....
Stationary Wigner Equation with In ow Boundary Conditions: Will a Symmetric Potential Yield a Symmetric Solution
Wigner equation In ow boundary conditions Well-posedness.
2014/9/26
Based on the well-posedness of the stationary Wigner equation with in
ow bound-ary conditions given in [1], we prove without any additional prerequisite conditions
that the solution of the Wigner eq...
匹配Wigner变换及其在瞬时频率估计中的应用
时频分布 多项式相位信号 匹配Wigner变换 瞬时频率估计 多普勒信号
2017/1/11
提出了一种新的时频分析方法,称为匹配Wigner变换(Matched Wigner Transform,MWT).该变换通过泰勒级数扩展傅立叶旋转因子e-jωτ来匹配双线性信号核,能够对单分量高阶多项式相位信号(Polynomial Phase Signal,PPS)分析得到聚集性最优的时频分布(Time Frequency Distribution,TFD),且克服了自交叉项的干扰.基于MWT,...
本文将经典Wigner-Ville分布(WVD)拓展到分数阶Wigner-Ville分布(FrWVD)，并将其引入到复杂地震信号的时频分析和谱分解中。利用分数阶傅里叶变换的旋转特性和广义时频带宽积理论可以获得比经典WVD更高的时频分辨率，提出的最优分数阶伪WVD能更好地解决交叉项抑制问题。理论信号仿真及实际地震资料的处理结果验证了该方法的有效性。同时，分数域频谱成像的引入为油气储层流体识别提供了一...
Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices
random matrices Wigner ensemble dilute random matrices
2011/9/22
Abstract: We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spect...
Multidimensional semicircular limits on the free Wigner chaos
Convergence in Distribution Fourth Moment Condition Free BrownianMotion Free Probability Multidimensional Limit Theorems
2011/9/21
Abstract: We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This...
Quark Wigner Distributions and Orbital Angular Momentum
Quark Wigner Distributions Orbital Angular Momentum
2011/7/21
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space. These functions can be obtained through a Fourier transform in the transve...
How universal is the Wigner distribution?
Wigner distribution universal Statistical Mechanics
2011/8/17
Abstract: We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial s...
Convergence of Wigner integrals to the tetilla law
Contractions Free Brownian motion Free cumulants Free probability Non-central limit theorems Wigner chaos
2011/9/14
Abstract: If x and y are two free semicircular random variables in a non-commutative probability space (A,E) and have variance one, we call the law of 2^{-1/2}(xy+yx) the tetilla law (and we denote it...