Quantum Theory and Its Stochastic Limit

L. Accardi, John Edward Gough, Y.G. Lu

Luigi Accardi, F. Gómez-Cubillo

This work is a detailed study of the convergence of the rescaled creation and annihilation densities, which lead to the master fields, and the form of the drift in the stochastic limit of quantum theory. The approach, based on the distributional theory of Fourier transforms, dispenses with the “analytical condition” and other restrictions usually considered and also establishes the dependence of the stochastic golden rules upon the dispersion function of the quantum field.

John R. Klauder

Luigi Accardi, F. Gómez-Cubillo

We apply new techniques based on the distributional theory of Fourier transforms to study, in the stochastic limit of quantum theory, the convergence of the rescaled creation and annihilation densities, which lead to the master fields, and the form of the drift term of the stochastic Schrodinger equation obtained in such limit. This approach permits us to dispense with the "analytical condition" and other restrictions usually considered and also to establish the dependence of the stochastic golden rules on certain properties of the dispersion function of the quantum field.

Sheldon Goldstein

Stuart D. Augustin, HERSCHEL A. RABITZ

Previous stochastic theory research has described individual molecular collisions by a master equation or a Fokker–Planck equation. The perturbation (weak coupling) limit of this theory is examined more carefully in this paper. It is shown how the formulation reduces to exact quantum mechanics in the perturbation regime. The methods are applied to the collinear forced quantum oscillator model for purposes of comparison with other theories. The results of this work and previous research show that stochastic collision theory firmly connects up to both the weak and strong coupling limits. It is suggestive that computationally attractive schemes which afford reasonable accuracy can now be developed for the intermediate coupling regime as well.