Related papers: Unifying distribution functions: some lesser known…
We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-functions. We then show the fundamental properties of these functions…
To overcome the impossibility of representing the energy of a signal simultaneously in time and frequency, many time-frequency representations have been introduced in the literature. Some of these are recalled in the Introduction. In this…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the 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 representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…
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 article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
The analytic properties of a class of generalized Husimi functions are discussed, with particular reference to the problem of state reconstruction. The class consists of the subset of Wodkiewicz's operational probability distributions for…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
In the context of nucleon structure, the Wigner distribution has been commonly used to visualize the phase-space distribution of quarks and gluons inside the nucleon. However, the Wigner distribution does not allow for a probabilistic…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…
In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of \hbar can be constructed for them without referring to the…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We demonstrate experimentally a novel technique for characterizing transverse spatial coherence using the Wigner distribution function. The presented method is based on measuring interference between a pair of rotated and displaced replicas…
Wigner distributions play a significant role in formulating the phase space analogue of quantum mechanics. The Schrodinger wave-functional for solitons is needed to derive it for solitons. The Wigner distribution derived can further be used…
We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and…