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Related papers: Local sampling of the SU(1,1) Wigner function

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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…

Quantum Physics · Physics 2015-06-16 Pier A. Mello , Michael Revzen

We revise the symmetries of the Zernike polynomials that determine the Lie algebra su(1,1) + su(1,1). We show how they induce discrete as well continuous bases that coexist in the framework of rigged Hilbert spaces. We also discuss some…

Mathematical Physics · Physics 2019-10-02 Enrico Celeghini , Manuel Gadella , Mariano A del Olmo

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…

High Energy Physics - Theory · Physics 2013-04-05 Stanislaw Mrowczynski

In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…

High Energy Physics - Theory · Physics 2009-10-02 Thomas Curtright , Tsuneo Uematsu , Cosmas Zachos

Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is…

Quantum Physics · Physics 2016-12-23 Roy Oste , Joris Van der Jeugt

The global symmetry data of a $D$-dimensional absolute quantum field theory can sometimes be packaged in terms of a $(D+1)$-dimensional bulk system obtained by extending along an interval, with a relative QFT$_D$ at one end and suitable…

High Energy Physics - Theory · Physics 2025-12-23 Jonathan J. Heckman , Max Hübner , Chitraang Murdia

We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of…

Quantum Physics · Physics 2013-11-05 Hai-Woong Lee

We measure complete and continuous Wigner functions of a two-level cesium atom in both a nearly pure state and highly mixed states. We apply the method [T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016)] of strictly constructing…

Quantum Physics · Physics 2018-01-26 Yali Tian , Zhihui Wang , Pengfei Zhang , Gang Li , Jie Li , Tiancai Zhang

Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…

Quantum Physics · Physics 2020-02-24 Bálint Koczor , Robert Zeier , Steffen J. Glaser

Undulator radiation from synchrotron light sources must be transported down a beamline from the source to the sample. A partially coherent photon beam may be represented in phase space using a Wigner function, and its transport may use some…

Accelerator Physics · Physics 2021-01-26 Boaz Nash , Nicholas Goldring , Jonathan Edelen , Stephen Webb , Rafael Celestre

We cast the phase state as a $SU(1,1)$ nonlinear coherent state to support the idea that the $SU(1,1)$ representation of the electromagnetic field may be helpful in some instances and to bring forward that it may relate to the phase state…

Quantum Physics · Physics 2014-06-05 F. Soto-Eguibar , B. M. Rodríguez-Lara , H. M. Moya-Cessa

We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides a direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function…

Quantum Physics · Physics 2009-10-31 Konrad Banaszek , Krzysztof Wodkiewicz

Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived,…

Quantum Physics · Physics 2017-05-19 H. A. Kastrup

We consider an arbitrary square integrable function $F$ on the phase space and look for the Wigner function closest to it with respect to the $L^2$ norm. It is well known that the minimizing solution is the Wigner function of any…

Mathematical Physics · Physics 2018-11-06 J. S. Ben-Benjamin , L. Cohen , N. C. Dias , P. Loughlin , J. N. Prata

The SU(1,1) interferometer can be thought of as a Mach-Zehnder interferometer with its linear beamsplitters replaced with parametric nonlinear optical processes. We consider the cases of bright and vacuum-seeded SU(1,1) interferometers…

Quantum Physics · Physics 2017-07-05 B. E. Anderson , B. L. Schmittberger , P. Gupta , K. M. Jones , P. D. Lett

In the framework of statistical optics, a Wigner function represents partially coherent radiation. A Gaussian Wigner function, which is an equivalent representation of the more commonly used Gaussian Schell-model cross-spectral density, may…

Accelerator Physics · Physics 2024-06-12 Ilya V. Pogorelov , Boaz Nash , Dan T. Abell , Paul Moeller , Nicholas Goldring

One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective. We introduce a…

Quantum Physics · Physics 2021-07-07 Lucas Kocia , Peter Love

The Wigner function is a well-known phase space distribution function with many applications in quantum mechanics. In this article, we consider an open quantum system consisting of a non-relativistic single particle interacting with a…

Quantum Physics · Physics 2026-05-06 Nick Huggett , Christian Käding , Mario Pitschmann , James Read

Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…

Quantum Physics · Physics 2020-06-19 Filippus S. Roux , Nicolas Fabre

In this thesis, we construct an approximate series solution of the Wigner equation in terms of Airy functions, which are semiclassically concentrated on certain Lagrangian curves in two-dimensional phase space. These curves are defined by…

Mathematical Physics · Physics 2017-06-13 Konstantina-Stavroula Giannopoulou