Generalized theory of interference, and its applications

S. Pancharatnam

Makoto Yamaguchi, Alexey Lyasota, Tatsuro Yuge

We propose a Markovian quantum master equation that can describe the Fano effect directly, by assuming a standard cavity quantum electrodynamics system.The framework allows us to generalize the Fano formula, applicable over the weak-and strong-coupling regimes with pure dephasing.A formulation of its emission spectrum is also given in a consistent manner.We then find that the interference responsible for the Fano effect is robust against pure dephasing.This is counterintuitive because the impact of interference is, in general, severely reduced by decoherence processes.Our approach thus provides a basis for theoretical treatments of the Fano effect and insights into the quantum interference in open quantum systems.

Richard B. Schulz

Arthur I. Fine

The aim of this paper is to present and discuss a probabilistic framework that is adequate for the formulation of quantum theory and faithful to its applications. Contrary to claims, which are examined and rebutted, that quantum theory employs a nonclassical probability theory based on a nonclassical “logic,” the probabilistic framework set out here is entirely classical and the “logic” used is Boolean. The framework consists of a set of states and a set of quantities that are interrelated in a specified manner. Each state induces a classical probability space on the values of each quantity. The quantities, so considered, become statistical variables (not random variables). Such variables need not have a “joint distribution.” For the quantum theoretic application, there is a uniform procedure that defines and determines the existence of such “joint distributions” for statistical variables. A general rule is provided and it is shown to lead to the usual compatibility-commutivity requirements of quantum theory. The paper concludes with a brief discussion of interference and the misunderstandings that are involved in the false move from interference to nonclassical probability.

Peter Hawkes, Erwin K. Kasper

Paul Sophus Epstein, P. Ehrenfest

In an important paper published on the pages of these PROCEEDINGS, W. Duane(1) makes a successful "attempt to formulate a theory of the reflection of X-rays by crystals, based on quantum ideas without reference to interference laws." A. H. Compton,(2) enlarging upon a hint contained in Duane's paper, has recently pointed out that the latter's hypothesis can be justified by the application of the general rules of the theory of quanta to the translatory motions of a crystal lattice.