32 research outputs found
Symplectic tomography as classical approach to quantum systems
By using a generalization of the optical tomography technique we describe the
dynamics of a quantum system in terms of equations for a purely classical
probability distribution which contains complete information about the system.Comment: 12 pages, LATEX,preprint of Camerino University, to appear in
Phys.Lett.A (1996
Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice
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 dimensional Hilbert
space, whose "phase space" is a lattice with sites, we get different
results depending on whether is odd or even. Under the new condition, the
Wigner function is determined if is an odd number, but it does not exist if
is even.Comment: 18 page
Wigner Functions on a Lattice
The Wigner functions on the one dimensional lattice are studied. Contrary to
the previous claim in literature, Wigner functions exist on the lattice with
any number of sites, whether it is even or odd. There are infinitely many
solutions satisfying the conditions which reasonable Wigner functions should
respect. After presenting a heuristic method to obtain Wigner functions, we
give the general form of the solutions. Quantum mechanical expectation values
in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE
Entropy and Wigner Functions
The properties of an alternative definition of quantum entropy, based on
Wigner functions, are discussed. Such definition emerges naturally from the
Wigner representation of quantum mechanics, and can easily quantify the amount
of entanglement of a quantum state. It is shown that smoothing of the Wigner
function induces an increase in entropy. This fact is used to derive some
simple rules to construct positive definite probability distributions which are
also admissible Wigner functionsComment: 18 page
Duality symmetry for star products
A duality property for star products is exhibited. In view of it, known
star-product schemes, like the Weyl-Wigner-Moyal formalism, the Husimi and the
Glauber-Sudarshan maps are revisited and their dual partners elucidated. The
tomographic map, which has been recently described as yet another star product
scheme, is considered. It yields a noncommutative algebra of operator symbols
which are positive definite probability distributions. Through the duality
symmetry a new noncommutative algebra of operator symbols is found, equipped
with a new star product. The kernel of the new star product is established in
explicit form and examples are considered.Comment: 14 pages, no figure