相关论文: The wave front set of the Wigner distribution and …
The second part of the article is devoted to field transfers by diffraction that are represented by fractional Fourier transformations whose orders are complex numbers. The corresponding effects on the Wigner distributions associated with…
This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short…
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be…
We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…
The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval…
In this paper we consider the Ito-Schrodinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the correlation length of the medium is…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
We investigate the Wigner distributions of $\bar{u}$ and $\bar{d}$ quarks in a proton using the overlap representation within the light cone formalism. Using the light cone wave functions which are obtained from the baryon-meson fluctuation…
We consider random Schr\"odinger equations on $\bZ^d$ for $d\ge 3$ with identically distributed random potential. Denote by $\lambda$ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$. The space and time variables…
Diffraction in time of matter waves incident on a shutter which is removed at time $t=0$ is studied in the presence of a linear potential. The solution is also discussed in phase space in terms of the Wigner function. An alternative…
We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…
We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…
The boost-invariant longitudinal space, defined by the parameter $\sigma=\frac{1}{2}b^-P^+$ can be studied from the Fourier transformation of distributions over the conjugate variable skewness $\xi$. We investigate quark Wigner…
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These…