Evolution of a quantum system subject to continuous measurement

The path integration method is used to describe the evolution of a quantum system subject to continuous (in time) measurement. It is shown that nonselective continuous measurement leads to a continuous increase in the degree of mixing of states. A scheme is developed for calculating a family of “partial” evolution operators that describe the dynamics of the system with allowance for the back reaction of the instrument, and a generalized unitarity condition for them is formulated. The general results are then applied to the case of spectral measurements of a harmonic oscillator. The nature of the mixing which arises as a result of such measurements is analyzed.