Orbital Maghetism in Two-Dimensional Integrable Systems

Abstract
We study orbital magnetism of a degenerate electron gas in a number of two-dimensional integrable systems, within linear response theory. There are three relevant energy scales: typical level spacing , the energy , related to the inverse time of flight across the system, and the Fermi energy . correspondingly, there are three distinct temperature regimes: microscopic ( ), mesoscopic ( )and macroscopic ( ). In the first two regimes there are large finite-size effects in the magnetic susceptibility , whereas in the third regime approaches its macroscopic value. In some cases, such as a quasi-one-dimensional strip or a harmonic confining potential, it is possible to obtain analytic expressions for in the entire temperature range.