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About 5,131 papers for “Wigner function”
T. Bar-on · Springer Link (Chiba Institute of Technology)
\n We construct a version of the discrete Wigner function (DWF) for any dimension. This DWF will be constructed from the continuous Wigner function (CWF). In addition, this DWF has many properties of the CWF.\n
Cited by 0
Jens Peder Dahl · Physica A Statistical Mechanics and its Applications · 1982
Cited by 41
Ijaz Durrani · 2026
Cited by 0Open access
Durrani, Ijaz · 2026
Cited by 0Open access
A. B. Klimov, Claudio Muñoz · Journal of Optics B Quantum and Semiclassical Optics · 2005
We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered.
Cited by 26
Annals of Physics · 1969
Cited by 15
O. Jonasson, I. Knezevic · 2015
Abstract We employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum relaxation, and the decay of spatial coherences (localization). Based on a particle-based solution to the Wigner transport equation with the model collision inte-gral, we simulate quantum electronic transport at 10K in a GaAs/AlGaAs superlattice and accurately reproduce its cur-rent density vs field characteristics obtained in experiment.
Cited by 0
M. Revzen · Foundations of Physics · 2006
Cited by 11
Yue Zhang, Shunlong Luo · Physics Letters A · 2021
Cited by 5
Arai, Shun · arXiv (Cornell University) · 2026
Cited by 0Open access
Ulrich Seyfarth, A. B. Klimov, Hubert de Guise et al. · Greater South Information System · 2020
In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.
Cited by 0Open access
Usenko, Constantin V. · arXiv (Cornell University) · 2004
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is applied as well to seek indications of specific quantum properties of quantum systems leading to impossibility of the classical approximation construction. Most of all, as such an indication the existence of negative values in Wigner function for specific states of the quantum system being studied is used. The existence of such values itself prejudices the probabilistic interpretation of the Wigner function, though for an arbitrary observable depending jointly on the coordinate and the momentum of the quantum system just the Wigner function gives an effective instrument to calculate the average value and the other statistical characteristics. In this paper probabilistic interpretation of the Wigner function based on coordination of theoretical-probabilistic definition of the probability density, with restrictions to a physically small domain of phase space due to the uncertainty principle, is proposed.
Cited by 0Open access
Adolf W. Lohmann, Markus E. Testorf, Jorge Ojeda-Castaneda · SPIE eBooks · 2017
There is barely any other invention which had more influence on optical sciences than holography. One of the major steps in developing Gabor’s original concept into a practical method for wavefront recording and reconstruction is marked by the introduction of the offset reference wave by E. Leith and J. Upatnieks. The ability to separate the object wavefront spatially from other parts of the reconstructed wave is the basis for numerous applications of holography. Holography also forms the theoretical framework for many other optical phenomena and techniques. This includes the design of diffractive optical elements as a specialized case of computer-generated holography. Interferometric techniques, which are also based on a coherent superposition of two wavefronts, can be interpreted as a holographic recording of a complex wavefront. Generalized holography, where the wavefront is recorded on arbitrary surfaces, serves as a framework for solving the inverse source problem and for understanding tomographic imaging techniques. The latter is closely related to synthetic aperture radar imaging and acoustic imaging, both of which expand the holographic principle beyond its use with optical radiation. The importance of holography has prompted numerous interpretations focused either on a rigorous analysis or a rather intuitive explanation. In this context, we mention Roger’s explanation of holography, which explains the recorded pattern of a Gabor in-line hologram as the superposition of the plane reference wave and the spherical wave originating from each object point. This essentially interprets the hologram as the superposition of Fresnel zone patterns.Another useful interpretation is the analysis of the Leith–Upatnieks offset hologram as a phase-modulated spatial carrier, where the phase modulation corresponds to the information that is lost in a conventional photographic recording. This interpretation also provides the basis for computer-generated holography, and in particular for the coding of complex amplitudes as detour holograms. This chapter presents an alternative explanation of holography based on the Wigner distribution function (WDF), which was originally published by E.Wigner in 1932 as a phase-space representation of quantum mechanical systems. The French scientist J. Ville would introduce it about 15 years later as a tool for signal processing. It is the fact that WDF combines insight into physical phenomena with signal processing capabilities that makes it unique among other time-frequency transformations. The WDF was introduced into optics primarily by the work of Bastiaans during the late 70s and early 80s.
Cited by 2
Moya-Cessa, Hector · arXiv (Cornell University) · 2002
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the position-momentum Wigner function to, in analogy, construct a number-phase Wigner function that, if summed over photon numbers gives the correct phase distribution and integrated over phase gives the right photon distribution.
Cited by 0Open access
Ulrich Seyfarth, A. B. Klimov, Hubert de Guise et al. · Greater South Information System · 2020
In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.
Cited by 0Open access
Luigi Barletti, Paolo Bordone, Lucio Demeio et al. · Physical review. E · 2021
We examine the effect of the decoherence-induced reduction of correlation length on a one-dimensional scattering problem by solving numerically the evolution equation for the Wigner function with decoherence proposed by Barletti et al. [J. Comput. Theor. Transp. 47, 209 (2018)2332-430910.1080/23324309.2018.1520732]. The numerical solution is achieved by the splitting-scheme algorithm, suitably modified to include the decoherence term. Three cases are examined, corresponding to a reflection-dominated regime, a transmission-dominated regime, and an intermediate one. The dynamic evolution of the Wigner function is followed until the separation process of the reflected and of the transmitted packets is complete and it is observed for three different values of the correlation length. The outcomes show a broadening and flattening of the Wigner function which becomes progressively more pronounced as the correlation length is decreased. This results in a reduced reflection at low energies and in a reduced transmission at high energies.
Cited by 0Open access
U. Seyfarth, A. B. Klimov, H. de Guise et al. · Quantum · 2020
In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext mathvariant="bold">Dedication</mml:mtext></mml:mrow></mml:math>: While this manuscript was under review, we learnt with great sadness of the untimely passing of our colleague and friend Jonathan Dowling. Through his outstanding scientific work, his kind attitude, and his inimitable humor, he leaves behind a rich legacy for all of us. Our work on SU(1,1) came as a result of long conversations during his frequent visits to Erlangen. We dedicate this paper to his memory.
Cited by 22Open access
H. M. Moya-Cessa · Journal of Optics B Quantum and Semiclassical Optics · 2003
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the position-momentum Wigner function to, in analogy, construct a number-phase Wigner function that, if summed over photon numbers gives the correct phase distribution and integrated over phase gives the right photon distribution.
Cited by 15Open access
В. С. Филинов, M. Bönitz, A. Filinov et al. · Lecture notes in physics · 2007
Cited by 12Open access
Antoine Royer · Physical Review Letters · 1985
An operational procedure is given for determining experimentally, in principle at least, the Wigner function for an ensemble of particles. This manner of "measuring" a quantum state, whether pure or mixed, via its Wigner function, seems the simplest possible, and closely parallels the method one might use in classical mechanics to determine a (true) phase-space probability density.
Cited by 76