Landau diamagnetism revisited

The problem of diamagnetism, solved by Landau, continues to pose fascinatin g issues which have relevance even today. These issues relate to inherent q uantum nature of the problem, the role of boundary and dissipation, the mea ning of thermodynamic limits, and above ail, the quantum-classical crossove r occasioned by environment-induced decoherence, The Landau diamagnetism pr ovides a unique paradigm for discussing these issues, the significance of w hich is far-reaching. Our central result connects the mean orbital magnetic moment, a thermodynamic property, with the electrical resistivity, which c haracterizes transport properties of material.