相关论文: Using the Wigner-Ibach Surmise to Analyze Terrace-…
Recently it has been recognized that the so-called generalized Wigner distribution may provide at least as good a description of terrace width distributions (TWDs) on vicinal surfaces as the standard Gaussian fit and is particularly…
The so-called generalized Wigner distribution has earlier been shown to be an excellent approximation for the terrace width distribution (TWD) of vicinal surfaces characterized by step-step interactions that are perpendicular to the average…
For more than three decades, measurement of terrace width distributions (TWDs) of vicinal crystal surfaces have been recognized as arguably the best way to determine the dimensionless strength $\tilde{A}$ of the elastic repulsion between…
The Pairwise Einstein Model (PEM) of steps not only justifies the use of the Generalized Wigner Distribution (GWD) for Terrace Width Distributions (TWDs), it also predicts a specific form for the Step Position Distribution (SPD), i.e., the…
In random matrix theory, the spacing distribution functions $p^{(n)}(s)$ are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics…
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…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
Correlations between energy levels can help distinguish whether a many-body system is of integrable or chaotic nature. The study of short-range and long-range spectral correlations generally involves quantities which are very different,…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an application, we give a formula expressing Reidemeister torsion as…
The Gibbs-Boltzmann distribution offers a physically interpretable way to massively reduce the dimensionality of high dimensional probability distributions where the extensive variables are `features' and the intensive variables are…
Wigner distribution function has much importance in quantum statistical mechanics. It finds applications in various disciplines of physics including condense matter, quantum optics, to name but a few. Wigner distribution function is…
Hypothesis Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical…
Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration…
The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…
We prove the Erdos-Turan equidistribution inequality, using a construction due to Chebyshev, Markov, and Stieltjes. The method is applicable in a more general setting. As an example, we state another inequality that can be proved using this…