Orbital Magnetism of a Single Charge: 100 Years Later

The first objective of my talk is to give a very short digest of main achievements in the theory of orbital magnetism 100 years after the publication of the famous paper by Ms. H.-J. van Leeuwen. In particular, I am trying to give a new answer to the old question: why this magnetism is so small in the high-temperature limit? For this purpose, the probability distribution of the orbital magnetic moment in the equilibrium state is calculated. Then, I demonstrate new results concerning the evolution of the magnetic moment from the equilibrium state when the magnetic field depends on time. More precisely, I consider a quantum charged particle in nonstationary homogeneous magnetic fields in the most general situations, when the field is described by means of the linear vector potential A=B(t)[-y(1+β), x(1-β)]/2 with arbitrary values of the gauge parameter β, which depends on the shape of solenoid. Systems with different values of β are not equivalent for nonstationary magnetic fields, due to different structures of induced electric fields. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mean values of the energy and magnetic moment can be quite different for different gauges, i.e., for solenoids of different shapes. One interesting result is a big increase of the magnetic moment for rapidly decreasing magnetic field. Also, nontrivial effects are discovered when the magnetic field changes its sign, even in the adiabatic case: a giant diamagnetism is predicted.