Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the possibility of classical orbital diamagnetism for an
  unbounded system --the Bohr-van Leeuwen Theorem   Recently [EPL, 86, (2009) 17001], we had simulated the classical Langevin
dynamics of a charged particle on the surface of a sphere in the presence of an
externally applied magnetic field, and found a finite value for the orbital
diamagnetic moment in the long-time limit. This result is surprising in that it
seems to violate the classic Bohr-van Leeuwen Theorem on the absence of
classical diamagnetism. It was indeed questioned by some workers [EPL, 89,
(2010) 37001] who verified that the Fokker-Planck (FP) equation derived from
our Langevin equation, was satisfied by the classical canonical density in the
steady state, obtained by setting d/dt=0 in the FP equation. Inasmuch as the
canonical density does not contain the magnetic field, they concluded that the
diamagnetic moment must be zero. The purpose of this note is to show that this
argument and the conclusion are invalid -- instead of setting d/dt=0 one must
first obtain the fundamental time-dependent solution for the FP equation, and
then calculate the expectation value of the diamagnetic moment, and finally
consider its long-time limit (i.e., $t \to \infty$). This would indeed
correspond to our numerical simulation of the dynamics. That this is indeed so
is shown by considering the simpler analytically solvable problem, namely that
for an unbounded plane for which the above procedure can be carried out
exactly. We then find that the limiting value for the expectation of the
diamagnetic moment is indeed non-zero, and yet the steady-state FP equation
obtained by setting d/dt=0 is satisfied by the canonical density. Admittedly,
the exact analytical solution for the sphere is not available. But, the exact
solution obtained for the case of the unbounded 2D-plane illustrates our point
all right. We also present some further new results for other finite but
unbounded surfaces such the ellipsoids of revolution.

13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org