Macroscopic Quantum Effects in Magnetic Systems: An Overview

Abstract

At the macroscopic level, we are used to the idea that a system (ensemble) which has available to it two or more different states may, under certain conditions, be represented as occupying not one or other of these states but rather a linear superposition: for example, an atom driven by an electromagnetic field may be in a linear combination of its ground (s) state and an excited (p) state, and its properties are then different from what they would be in either state separately (e.g., the expectation value of the atomic polarization is zero in either an s-state or a p-state, but nonzero for the linear combination). Thus we say that in such atomic-level situations no “actualization” of one state or the other has taken place: formally, the linear-superposition state

$$\matrix{ {{\psi _{at}} = \alpha |s\rangle + \beta |p\rangle ,} & {|\alpha {|^2} + |\beta {|^2}} \cr } = 1$$

((1))

cannot be interpreted as indicating the occurrence of either an s or a p state for each particular member of the ensemble with probability |α|² (|β|²).