An Alternative Approach to Open Quantum Systems

Abstract

The dynamics of open quantum systems is described by a stochastic process that comes from the inevitable interaction between the system and its environment. More precisely, the environment is chosen as an external system which may have a finite or an infinite number of degrees of freedom. We analyse here how the orbital degrees of freedom (position, momentum) of a system represented by a coherent state of the quantum harmonic oscillator coupled with an in-homogeneous magnetic field can suffer transitions when a sequence of measurements if performed in its spin degree of freedom. In other words, the situation is as if the orbital degree of freedom represents a system of interest and the possible outcomes of such a measurement process represents a stochastic source. We shall explicitly show, using an analysis based on the concept of quantum trajectories, that it is a problem to which an analytical solution could be obtained to all relevant physical quantities. Moreover, we could derive an equal-probability rule for the state of our system: similar to the central a priori postulate of statistical mechanics. Through our analytical expressions and a numerical analysis, we could also determine that the continuous measurement process, in general, raises the mean energy of the system keeping its mean position and mean momentum invariant at the cost of making the distribution of their uncertainties broader.