  We investigate the low mass limit of Langevin dynamics for a charged Brownian
particle driven by the magnetic Lorentz force. In the low mass limit, velocity
variables relaxing quickly are coarse-grained out to yield effective dynamics
for position variables. Without Lorentz force, the low mass limit is equivalent
to the high friction limit. Both cases share the same Langevin equation that is
obtained by setting the mass to zero in the original Langevin equation. The
equivalence breaks down in the presence of the Lorentz force. The low mass
limit turns out to be singular. The system in the low mass limit is different
from the system with zero mass. The low mass limit is also different from the
large friction limit. We derive the effective equations of motion in the low
mass limit. The resulting stochastic differential equation involves a nonwhite
noise whose correlation matrix has antisymmetric components. We demonstrate the
importance of the nonwhite noise by investigating the heat dissipation by the
Brownian particle.
