DYNAMICS AND THERMODYNAMICS OF A SYSTEM OF MESOSCOPIC METALLIC RINGS

The persistent current of a system of isolated mesoscopic rings is calculated. In such a system one has to average over impurities, keeping the number of particles in each ring constant. We show that, although a standard thermodynamic formula for the persistent current gives different results depending on whether the calculation is done with a fixed number of particles or with a fixed chemical potential, a dynamic response is not sensitive to the averaging procedure. This allows us to do a calculation with a fixed chemical potential, which is a simpler task because well-developed methods of statistical physics based on Green functions exist. This is true also for interacting systems. Knowing the dynamic response we can calculate the persistent current, taking the limit of zero frequency and integrating over the magnetic field. Using the supersymmetry method we calculate the persistent current for a system of noninteracting particles and make comparisons with results of other analytical and numerical works.