Related papers: Wigner function for SU(1,1)
In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding…
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…
It is shown how a physical function, namely the Wigner function, that in principle may be measured, can be used to evaluate divergent series.
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators. We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the…
We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group…
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…
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…
By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group $\mathrm{SU(N)}$, it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete…
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…
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…
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency…
A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which…
We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our…
In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum…
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…
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the…
Given a real-valued phase-space function, it is a nontrivial task to determine whether it corresponds to a Wigner distribution for a physically acceptable quantum state. This topic has been of fundamental interest for long, and in a modern…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We present the reconstruction of the Wigner function of some classical pulsed optical states obtained by direct measurement of the detected-photon probability distributions of the state displaced by a coherent field. We use a photodetector…
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…