MESOSCOPIC ORBITAL MAGNETISM IN AN INTEGRABLE SYSTEM

Abstract

We study the mesoscopic orbital magnetism of a free electron gas in a rectangular box in the zero-temperature limit. We find that, as in weakly disordered systems, it can be well-described by the van Vleck susceptibility that couples just two size-quantized energy levels: the Fermi (last occupied) level and the first unoccupied level. Large fluctuations of the off-diagonal matrix elements of the angular momentum and, more importantly, of the nearest level spacings — level bunching characteristic of classically integrable systems — are responsible for the absence of effective self-averaging in this system. We develop a detailed analytical description and conduct extensive numerical simulations based on a combined averaging over the energy spectrum, and over the aspect ratio of rectangles with equal areas.