Remark on the decay of a mixed state

Abstract

The initial decay rate of a mixed state is discussed; is shown to be zero for finite energy states. In the previous paper [1] we investigated a general scheme for description of unstable systems. One of our results concerned the initial decay rate. Generalizing the earlier results ofHorwitz andMarchand (see [2] and other references contained in [1]) we proved there, that the initial decay rate of any pure state of the unstable system equals to zero, if this state is so called finite energy state.

Here we shall be interested in the same problem, assuming now the state of the decaying system to be in generalmixed. Such assumption seems to be reasonable: firstly, from the point of view of an experiment it is too restrictive to treat only pure states of unstable systems. In particular, mixed states are generally considered in the recent studies about the influence of measuring devices on the time evolution of the unstable system [3]. Moreover, for this kind of problems the behaviour of the unstable system immediately after its preparation, especially the initial decay rate, is of great importance (see also [4, 5]).

We shall prove in this paper that for finite energy states the initial decay rate is equal to zero, which generalizes the result contained in [1].