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A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and…

Quantum Physics · Physics 2007-05-23 S. Chaturvedi , E. Ercolessi , G. Marmo , G. Morandi , N. Mukunda , R. Simon

We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…

Quantum Physics · Physics 2008-03-31 Cecilia Cormick , Juan Pablo Paz

We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the…

Quantum Physics · Physics 2020-07-09 René Schwonnek , Reinhard F. Werner

The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…

Mathematical Physics · Physics 2015-12-09 Nicolae Cotfas

We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under…

Quantum Physics · Physics 2015-06-26 Miguel Angel Alonso , George S. Pogosyan , Kurt Bernardo Wolf

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

We show that there is a way to unify distribution functions that describe simultaneously a signal in space and (spatial) frequency. Probably the most known of them is the Wigner distribution function. Here we show how to unify functions of…

Wigner distributions for quantum mechanical systems whose configuration space is a finite group of odd order are defined so that they correctly reproduce the marginals and have desirable transformation properties under left and right…

Quantum Physics · Physics 2009-11-10 N. Mukunda , S. Chaturvedi , R. Simon

For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner…

Quantum Physics · Physics 2021-05-11 E. E. Perepelkin , B. I. Sadovnikov , N. G. Inozemtseva , E. V. Burlakov

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a…

Mathematical Physics · Physics 2015-05-18 Manas K. Patra , Samuel L. Braunstein

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner…

Mathematical Physics · Physics 2009-10-27 S. M. Nagiyev , G. H. Guliyeva , E. I. Jafarov

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…

Quantum Physics · Physics 2023-11-03 Federico Cerisola , Franco Mayo , Augusto J. Roncaglia

In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase…

Quantum Physics · Physics 2009-11-07 Minoru Horibe , Akiyoshi Takami , Takaaki Hashimoto , Akihisa Hayashi

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density…

High Energy Physics - Theory · Physics 2007-05-23 Aurelian Isar

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…

Quantum Physics · Physics 2009-10-30 G. M. D'Ariano , S. Mancini , V. I. Man'ko , P. Tombesi

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…

Mathematical Physics · Physics 2014-11-20 C. Bastos , N. C. Dias , J. N. Prata

We set up Wigner distributions for $N$ state quantum systems following a Dirac inspired approach. In contrast to much of the work on this case, requiring a $2N\times 2N$ phase space, particularly when $N$ is even, our approach is uniformly…

Quantum Physics · Physics 2015-05-14 S. Chaturvedi , N. Mukunda , R. Simon

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…

Quantum Physics · Physics 2009-11-10 Constantin V. Usenko

The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su_q(2). The spectrum of position in this discrete…

Mathematical Physics · Physics 2009-11-10 Natig M. Atakishiyev , Anatoliy U. Klimyk , Kurt Bernardo Wolf

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…

Quantum Physics · Physics 2026-01-28 Ramkumar Radhakrishnan , Vikash Kumar Ojha