Relaxation Phenomena in Spin and Harmonic Oscillator Systems

Abstract

A method is developed for generating relaxation by introducing a fundamental interval $\tau$ and a stirring hypothesis. The application to spin and harmonic oscillator systems is discussed in some detail. All the results are obtained by exact calculations without applying perturbation theory as the systems considered are simple and completely soluble. Equations similar to phenomenological Bloch equations are derived in the case of spin systems. The relaxation times obtained by the application of the theory are not only proportional to the strength of interaction, but also to the fundamental interval $\tau$ which plays an important role in the theory. It is shown that in the case of a harmonic oscillator system, an initial Boltzmann distribution relaxes to a final equilibrium Boltzman distribution through a sequence of transient Boltzman distributions.