Universal fluctuations in orbital diamagnetism: A surprise in theoretical physics

Over the last century Bohr van Leuween theorem attracted the notice of physicists. The theorem states about the absence of magnetization in classical systems in thermal equilibrium. In this paper, we discuss about fluctuations of magnetic moment in classical systems. In recent years this topic has been investigated intensively and it is not free from controversy. We a have considered a system consisting of a single particle moving in a plane. A magnetic field is applied perpendicular to the plane. The system is in contact with a thermal bath. We have considered three cases: (a) particle moving in a homogeneous medium, (b) particle moving in a medium with space dependent friction and (c) particle moving in a medium with space dependent temperature. For all the three cases average magnetic moment and fluctuations in magnetic moment has been calculated. Average magnetic moment saturates to a finite value in case of free particle but goes to zero when the particle is confined by a 2-D harmonic potential. Fluctuations in magnetic moment shows universal features in the presence of arbitrary friction inhomogeneity. For this case the system reaches equilibrium asymptotically. In case of space dependent temperature profile, the stationary distribution is non-Gibbsian and fluctuations deviate from universal value for the bounded system only.