Unified formalism for quantum and classical scattering theories

Fisica del Espacio

Based in some mathematical theorems, related to Lax-Phillips scattering theory, a unified (classical-quantum) formalism is introduced to explain the appearance of irreversibility in some class of systems (KLPS-systems). These systems are endowed with a unitary evolution that maps densities into densities, and they have a fixed subsystem in which this evolution is strongly contracting, yielding a Lyapounov variable and a unique equilibrium state. A global model of these systems is also studied.

K. N. Joshipura, Nigel John Mason

Murray Sargent, David A. Holm, Muhammad Suhail Zubairy

We present a theory that describes how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear two-level medium. The analysis is applicable to several popular problems with and without cavities. In particular, the theory treats laser and optical bistability instabilities, predicting when the instabilities grow from spontaneous emission. The theory is a multimode extension of Scully-Lamb theory that derives the equations that describe population pulsations, combination tones, mode locking, resonance fluorescence, Rayleigh scattering, and phase conjugation with quantum-mechanical fields. Hence the theory both presents new results on instabilities and phase conjugation, and also unifies the treatment of a variety of phenomena in the context of Lamb theory. The present paper (first of the series) presents the basic formalism, leaving most applications to subsequent papers in this series. The following paper presents equivalent derivations based on a purely operator formalism.

A.S. Davydov

J S Briggs, James M. Feagin

Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from sources at macroscopic distance and measured at macroscopic distance from the microscopic reaction volume. Standard experimental procedure is to describe asymptotic particle motion by classical mechanics. However, this transition to classical mechanics is not accounted for in standard quantum scattering theory. Hence, we revisit conventional scattering theory with the introduction of semiclassical propagators to describe the wave function in both incident and outgoing asymptotic scattering channels. This description leads to the manifestation of classical trajectories in the quantum wave function both before and after the collision. It includes the case of extraction with external fields as in modern multi-particle detectors. We derive the asymptotic Kemble imaging theorem (IT) limit to demonstrate how formal quantum scattering theory contains implicit classical mechanics threaded throughout the asymptotic wave functions.