Measurement Theory in Lax-Phillips Formalism

TL;DR

This paper explores how Lax-Phillips scattering theory can model quantum measurement and decoherence, revealing conditions under which decoherence occurs in closed and open systems, and connecting to the Many-Hilbert-Space theory.

Contribution

It demonstrates the application of Lax-Phillips formalism to quantum measurement, linking decoherence to Hamiltonian time-dependence and system openness, extending existing theories.

Findings

Decoherence requires time-dependent Hamiltonian in pointwise evolution.

Decoherence can occur in closed systems in Liouville space.

Lax-Phillips theory provides a natural framework for quantum measurement analysis.

Abstract

It is shown that the application of Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the Many-Hilbert-Space theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states.