The Wigner phase-space description of collision processes

M. Kira, S. W. Koch

María F. González, Josep María Bofill, Xavier Giménez

The tunnel effect in one-dimensional collision problems is analyzed in terms of numerical wavepacket time propagations, in position, momentum, and phase space representations of the problem. Bohm's total potential is used to provide a classical-like description of tunnelling quantum dynamics, under a time- and density-dependent potential. Wigner, Husimi, as well as Bohm phase space distributions are used in the present study, with their relative performances for the present problem having been analyzed.

Juan Pablo Paz

We present a phase-space description of the process of quantum teleportation for a system with an N-dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones. This function is useful to represent a composite quantum system in phase space and to analyze situations where entanglement between subsystems is relevant (dimensionality of the space of states of each subsystem is arbitrary). We also describe how a direct tomographic measurement of this Wigner function can be performed.

Daniel Lagolnitzer

Max Born

J.S. da Veiga

We extend the Weyl-Wigner transformation to include the second quantization scheme by introducing the Bargmann mapping kernel in the Weyl transform. Besides, we construct a holomorphic phase space in which complex entire analytic functions of two variables, namely, z and w*, stand for the boson creation and annihilation operators representatives, respectively. The dynamical equations are obtained by the mapped Heisenberg equation of motion. So, a holomorphic expression for an excitation probability is presented and an explicit calculation is performed for the forced harmonic oscilator. Finally, we apply the holomorphic phase-space description to a particular collision process, i.e.,the analytical study of the Coulomb excitation for the isovector giant electric dipole ressonance in the eikonal approximation. Comparisons with experimental results are presented and discussed